My Next Car: Pay Cash, Borrow or Lease?

The finances of buying a car can be tricky.  In addition, there are so many other things to consider. What kind of car do I like?  How often do I want to replace my car?  How many people (and pets) do I need to be able to transport comfortably?  Through what weather conditions do I need to drive? Do I want a new or used car (as discussed here)? In this post, I’ll focus on the finances of purchasing a car once you’ve decided generally what car(s) fit your other needs.  Specifically, I’ll describe the financial considerations of three options for buying your next car: pay cash, borrow or lease. I will also provide a spreadsheet to allow you to compare the finances of specific deals.

The Basics of Leases and Loans

I have a post that provides all the basics you need to understand about loans.

There are plenty of resources available to provide you with information about leases, so I won’t repeat that information here.  Here are a few resources:

  • This article focuses on teenagers, but it covers a lot of important aspects of leasing. Consumer Reports is considered an independent source for information about purchases.
  • Edmunds is a company that values and researches cars, as well as having a platform for selling used cars. Its guide on leasing can be found here.
  • The first several sections of this post by Debt & Cupcakes (@debtandcupcakes) provide details about leasing, along with the pros and cons.
  • Real Car Tips also has a guide for leasing. Here is the link for the leasing guide.

Your credit score is an important driver of the terms you will be offered whether you lease or borrow.  When I looked for examples on line, all of the offers were contingent on your credit score being above 800.  A credit score of 800 is excellent.  I have a post on how you can check and improve your credit score.

The Finances of Owning a Car

Cars are expensive to own.  This post will focus on the cost of buying a car under three different options – cash, borrowing and leasing.  As you evaluate which of the options works for you, you’ll also want to make sure you are able to afford the other costs of ownership of a car.  In addition to the purchase costs discussed below, there are four other categories of expenses:

Fuel

Your car needs gas, diesel or electricity.  As you are selecting a car, you’ll want to consider the type of fuel your car needs, the miles per gallon the car gets and how many miles you are going to drive.

Registration

You will need to register your car every year.  In the states in which I’ve owned cars, registration is a function of the value of the car – the higher the value, the higher the registration fees. I recall that a car worth $20,000 cost about $300 to $400 a year to register, whereas the minimum charge (for older cars) was about $50 a year in Minnesota, but the amounts vary widely across states.  In other states, registration fees are a flat amount regardless of the age or value of your car.

Insurance

In all states you are required to buy car insurance. This post provides information on insurance you are required to purchase and coverages you might want to purchase.  Liability insurance usually doesn’t depend on the value of the car, though can be higher for sportier and faster cars.  The premiums for physical damage coverages (comprehensive and collision which protect you against damage to your car) increase with the value of your car.

Maintenance & Repairs

Cars need regular maintenance – oil changes, replacement brakes and tires, among other things.  Some dealers provide regular maintenance at their location for one or more years if you buy a new car, but that is not always the case.  In addition to regular maintenance, cars break down and need to be repaired.  Repair expenses tend to be higher on older cars.  Even on new cars, repairs can be expensive and unexpected.

You’ll want to keep some money in your designated savings for car repairs, as discussed in this post.  Another option is to buy an extended warranty to cover repairs to your car.  Extended warranties can be quite expensive, but cover the cost of some major repairs if they are needed.  I’ll write about extended warranties in another post in the future. If you choose to purchase an extended warranty, you’ll need to include that cost as part of your expenses related to owning the car, along with a provision for repairs not covered by the warranty.

How to Think About the Finances of Buying a Car

Determine Your Needs

I always find it helpful to define what I want and can afford before I go shopping for anything expensive, cars in particular.  My husband does all of the negotiating on price for our cars because that is a skill I never acquired and I don’t like the process so don’t want to acquire it.  I figure out what I need, what’s available in our price range that meets those needs and make a very detailed list so he can go to different dealers to negotiate the terms.

As part of your needs, you’ll want to think about the length of time you’d like to own your car.  Some people like to drive a new or at least a different car every few years.  I was that way when I was young – I bought a different car every 3 years for a bit.  I’ve always regretted selling the first one – a 1969 Mustang convertible. Live and learn!

Other people drive cars until they die or become unreliable.  Now that I understand the finances of cars better, I have moved to the second category.  The most recent two cars I’ve sold (both Honda Preludes) had 250,000 and 150,000 miles on them respectively.  The only reason I sold the second one is because I moved to a place with hills and snow, as opposed to flat and snow, and a Honda Prelude just wasn’t going to get me home reliably in the winter.

Figure Out What You Can Afford

The second step in the process – figuring out what’s in your price range – can involve several perspectives.

  1. How much cash do you have available to either pay for the entire car or put as an initial payment towards a loan or lease? As you consider that amount, you’ll want to take the total cash you have available and reduce it for the other costs of ownership I’ve listed above.
  2. If you aren’t going to pay cash for the car, how much you can afford to pay every month? Again, don’t forget that you’ll need to pay for registration, insurance, fuel, maintenance and repairs, too.
  3. If you can’t find new cars that fit in your budget, you might need to look at used cars. I have another post planned that will address the finances of buying new versus used.

Gap Insurance

Gap insurance is another expense you may have to pay if you don’t pay cash for your car. In some cases, you’ll want to buy it for your peace of mind.  In other cases, the lender or lessor may require it.

Gap insurance protects you against the difference between the value of the car and your outstanding balance at any point in time during the loan or lease.  Although it may not be clearly stated in your lease agreement, lessors think of your lease payments as including compensation to them for the reduction in the value of the car as you use it (depreciation) and interest on the value of the car (similar to loan interest).  As such, both loans and leases have outstanding balances at all times during their terms.

The chart below compares the outstanding balance on a loan with an estimate of the value of a $23,000 car over the term of an 84-month loan.  For this illustration, I’ve assumed that the borrower paid $1,000 towards the value of the car as a down payment and the loan has a 3% interest rate. I estimated the value of the car by looking at the clean trade-in value of a Ford Fusion from prior model years on the National Automobile Dealers Association (NADA) web site, a common source for lenders to get car values.

For the Ford Fusion, the loan balance is more than the value of the car between 4 and 36 months.  If the car is totaled, your car insurer will reimburse you for the value of the car minus your deductible.  During that time period, you will owe the lender not only your deductible but the difference between the blue line and the orange line.  To protect yourself from having to pay the additional amount, you can buy gap insurance.

You’ll want to investigate the cost and need for gap insurance for the particular make and model you are buying.  Cars depreciate at different rates.  For example, when I looked at the NADA web site for a Subaru Impreza, the value never went below this illustrative loan balance.

The Finances of Cash, Leases and Borrowing

Now that I’ve covered the preliminaries, we can get to the main topic of this post – the details of paying cash, borrowing and leasing.

Cash

When you pay cash for a car, there is only one number on which you need to focus. It is the out-the-door cost of buying the car.  This amount will include some or all of the following:

  • The cost of the car,
  • The additional cost of options you choose,
  • Sales tax (called excise tax in some jurisdications),
  • Processing and documentation fees,
  • Delivery charges, and
  • Title and registration fees.

Not all of these charges are included in every state or by every dealer.  I recently bought a new car in Montana. There is no sales tax in Montana, there wasn’t a delivery charge and you pay the state for title and registration fees directly, so the only things on my invoice were the cost of the car, the cost of the two options I added and a $100 documentation fee.  If you are comparing prices from different sources, you’ll want to make sure that they consistently treat all of these possible costs. For example, you should make sure they either all include or all exclude title and registration fees.   If not, you’ll need to add them to your analysis of the total amount you can pay for the car.

Leasing

The finances of leasing involve many important numbers, even more than borrowing.  All of these numbers should be available to you in the contract and from the dealer or leasing company. 

Up-front Payment

You’ll want to make sure you know the total amount of the up-front payment, including sales taxes, title and registration fees and the base charges from the dealer and finance company. The up-front payment often includes the first month’s lease payment, but not always, so you’ll want to be sure to know whether it is included for each offer you consider.

Monthly Payment

The amount that you’ll pay every month.

Sales Tax Rate

You pay sales tax on your monthly lease payments.You’ll need to know if the sales tax is included in the monthly payment you’ve been quoted and, if not, what sales tax rate applies.

Term

The term is the number of months you are committed to the lease. It is important to note that my spreadsheet assumes the lease term is 36 months and you will honor your commitment to the lease for its entire term.  There can be significant penalties if you choose to return the car before the lease ends.

Allowed Annual Mileage

Every lease contains a maximum number of “free” miles you can drive on average each year.

Estimated Actual Annual Mileage

You can use your actual annual mileage to estimate how much you will have to pay in excess mileage charges to understand the full cost of a least.

Cost Per Extra Mile

If you exceed the total allowed mileage (the allowed annual mileage times the term), you will pay an extra fee when you return the car. To calculate the extra amount, you first take your actual mileage and subtract the total allowed mileage.  You then multiply the excess miles by the cost per extra mile.  As I’ve looked on line at leases, I’ve seen several that charge 15 cents per extra mile.  If, for example, you drive 50,000 in three years on a car with 12,000 miles allowed and a 15 cent per mile charge, you will pay an extra $1,800 when the lease ends.

You may also need to pay a fee if your car experiences more than the normal amount of wear and tear. For example, if you live on a gravel road or a busy street, your car may have many more nicks and dings than someone who lives on a quiet paved cul-de-sac.

Residual Value

If you think you might want to buy the car at the end of the lease, you’ll need to know the residual value.This amount is what you will pay to keep the car.

Monthly Cost of Gap Insurance

If you want or need to buy gap insurance, you’ll want to know by how much it costs each month. You can buy gap insurance from your car insurer and, sometimes, the dealer, though I’ve read that buying it through the dealer tends to be more expensive.

Borrowing

The finances of taking out a loan for a car are a bit less complex than leasing. Here are the important numbers you need to know.

  • Up-front payment – You’ll want to make sure you know the total amount of the up-front payment, including sales taxes, title and registration fees and the base charges from the dealer and finance company. The up-front payment often includes the first month’s lease payment, but not always, so you’ll want to be sure to know whether it is included for each offer you consider.
  • Amount financed – This amount is equal to the total value of the car minus the portion of your up-front payment that goes towards paying for your car.
  • Monthly payment – The amount that you’ll pay every month. There is no sales tax on loan payments.  The sales tax was considered in the total amount of the car used to determine your up-front and monthly payments.
  • Interest rate – The interest rate, along with the amount financed and monthly payment, are used to determine the remaining principal on your loan at point in the future. If you want to sell your car before you have paid off your loan, you’ll want to be sure to know the amount financed and the interest rate so the spreadsheet can calculate the remaining principal.
  • Loan term – The term determines how many monthly payments you will make.
  • Monthly cost of gap insurance – If you need or want to buy gap insurance, you’ll want to know by how much it costs each month.

Illustrative Comparison

Because I just purchased a Subaru Impreza for around $23,000, I use it and two other cars advertised as having similar costs as illustrations.

The Offers

The table below summarizes the values I found on line and/or created for a Subaru Impreza, a Toyota Camry and a Ford Fusion

Although the cash prices are similar, the Lease and Borrow options have fairly different terms. The amount due at signing and monthly payment are much lower for the Toyota Camry lease than for the other two cars. The interest rates on the loans are very different, even though the monthly payments are all essentially identical. The Subaru has a lower interest rate and shorter term than the other two cars.  Because the payments are the same and the interest rate is higher, the amount due at signing must cover more of the cost of the Toyota than for the other two cars.

Not all of these values were clearly identified in the terms I found on-line.  The actual offers could be somewhat to significantly different from the values I’ve shown above.  Nonetheless, the differences in the terms help differentiate the total financial cost of these offers.

Look at Just the Subaru

We will first look at a comparison of the three options for the Subaru Impreza. Before we can do that, you need to determine for how long you want to own the car.  For illustration, I’ve looked at two options – own it for the term of the lease (assumed to be 36 months) or own it until it dies (or at least until you’ve made all of your loan payments).

Sell in Three Years

The first row of the table below shows the total of all of the payments you will make under each of the three options over the course of the first three years.  For the Cash option, it is your out-the-door cost. For the Borrow and Lease options, it is the sum of the amount due at signing, your monthly payments and the monthly cost of gap insurance.  For the Lease option, I added sales tax to the monthly lease payments.

Three Years Cash Borrow Lease
Upfront Cost + Monthly Payments $23,691 $14,133 $15,971
Amount on Sale 12,000 761 -1,350
Net Cost 11,691 13,372 17,321

The second row shows how much you would get or pay at the end of 36 months.  For all three cars, I have assumed you can sell them for $12,000 after three years. For the Cash option, the second row shows the total sales price of the car.  For the Borrow option, it is the difference between the $12,000 sales price and the loan balance.  For the Lease option, the value is negative meaning it is an amount you have to pay instead of receive.  It is the charge for the extra miles put on the car.  If you look at the inputs table, you’ll see that there is a 15 cent per mile charge for every mile over 12,000 a year and I have assumed you will drive 15,000 miles a year.

The third row shows the total net cost, calculated as the first row minus the second row.  For the offers for the Subaru Impreza, the Cash option is cheapest if you plan to sell after 3 years.  If you can’t afford to pay cash up front, the Borrow option is preferred to the Lease option.

Drive Forever

Under the Drive Forever option, the sales price of the car is assumed to be essentially zero, so we can look at just the cash outflows.  The table below summarizes the total cost of the three options.

Drive Forever Total Cost
Cash $23,691
Borrow 25,581
Lease 31,321

The total cost of the Cash option is the same as in the Three Years table.  There are no purchasing costs other than the amount paid at signing under this option.  For the Borrow option, the total cost has increased from the Three Years option because it now includes the monthly payments after three years until the loan is fully re-paid.  For the Lease option, the cost has increased by the residual value of the car, $14,000 in this case.  That is, in addition to the up-front and monthly lease payments, you’ll need to pay the $1,350 for the extra miles and $14,000 to buy the car from the lessor.

Using the longer time frame, the Lease option is even more expensive than the Borrow option.  Because the interest rate is fairly low, the additional interest paid after three years isn’t a lot so the difference between the Borrow and Cash options doesn’t increase by a large amount from what was observed for the Three Years option.

Look at All Three Cars – Three Years

The relative order of the three options varies depending on the terms of the offer. The graph below compares the net costs of ownership of the three cars if you anticipate selling the car in three year.

The values for the Subaru Impreza are the same as the ones in the third row of the Three Years option table above.  As can be seen, leasing isn’t always the worst option as was the case for the Subaru. The Lease option is less expensive than the Borrow option for the Camry and is only slightly more expensive than the Borrow option for the Ford, using the three-year time frame.

If you are indifferent among the three cars, you could also compare the costs among the cars.  For example, let’s say you don’t have enough cash to pay for the car up front, so you are looking at the Lease and Borrow options. The net cost of the Lease option for the Camry is about the same as the Borrow option for the Impreza.  The risk of the Lease option is that you will drive even more miles than you’ve estimated adding to the net cost of the Camry Lease option.  You would want to offset that risk with the risk that you might not get $12,000 for the Impreza when you sell along with the hassle of having to sell the Impreza.

This comparison highlights the importance of getting all of the detailed terms of every option.

Look at All Three Cars – Drive Forever

The graph below shows the same comparison for the “Drive Forever” option.

Other than the total costs of ownership being higher (because you are owning the car until it dies instead of having to replace it or selling it in three years), the relationships among the three options for each car are essentially the same. That is, the order and relative costs of the Cash, Borrow and Lease options are the same for each vehicle.

Of the Lease and Borrow options, the Impreza Borrow option is the least expensive in this example.  The Camry Borrow and Lease options and Ford Borrow option are all $3,000 to $4,000 higher, so you might choose from one of those if you didn’t like the Impreza.  If you have cash to buy the car outright, the Ford Cash option is the least expensive, though the Camry is only a few hundred dollars more.

In addition to comparing different makes and models, you can make similar comparisons among offers you obtain from different dealerships for the same car.

Can I Invest my Cash and Use it to Pay Off my Lease or Loan?

For those of you who read my post about Chris’s mortgage, you know that I suggested he consider paying the minimum payments on his mortgage and investing the rest of his money.  You may be wondering why I haven’t talked about the benefits of investing money under the Lease and Borrow options.

There are a few reasons.

  • Most people who buy a car using a lease or borrowing don’t have the cash available to pay for the car up front. If you don’t have cash to invest, there is no possibility of investment returns.
  • The term of a lease or loan is much shorter than the length of a fairly new mortgage. In Chris’s case, he had 26 years of payments left on his mortgage.  As I discussed in my post on investments and diversification, the likelihood you will earn the average return increases the longer you invest. With the short time span of a car loan or lease, investing in stocks with the expectation of having money to pay off your lease or loan would be very risky.  There is a fairly high probability your investments wouldn’t return enough to make those payments.
  • To avoid the chance that your investments wouldn’t cover your car payments, you could invest in something with very low risk, such as a money market account, certificates of deposit (of which you would need a lot to match the timing of your loan or lease payments) or high yield savings account. Low risk investments currently have very low returns – generally less than 2.5% pre-tax and even less than that after tax.  There are very few loans or leases that have interest rates (implicit in the case of a lease) that are less than 2.5%, so there isn’t much benefit in investing cash in risk-free assets until your loan or lease payments are due.

How To Use the Spreadsheet

To help you create your own comparisons similar to the ones above, I’ve provided you my spreadsheet at the link below.

Overview

The flowchart below will help guide you through the financial aspects of the car-buying process.  It assumes that you have identified one or more cars that will meet your needs and possibly fit in your budget.

The hexagonal boxes in a flow chart correspond to decision points. The rectangular boxes contain action items.

The first step is to determine whether you can afford to pay cash.  If not, you won’t have to negotiate a price for the Cash option for any of the cars you are considering.

Next, take a look at estimates of the up-front and down payments for the Lease and Borrow options.  If you can’t afford either of them in addition to the other costs of car ownership, you will need to find a less expensive option – either new or used – and go back to the top of the flowchart.

The next decision point is how long you want to own the car – the term of the lease (which I have assumed will be three years) or a much longer time (at least as long as the term of the loan in the Borrow option).  When you are done entering the values, you’ll look at the summary at the top of the Lease Term tab if you plan to own the car for the lease term and the Drive Forever tab if you want to own it longer.

If you want to own the car beyond the end of the lease, you’ll need to be able to afford to pay the residual value at the end of the lease.  If not, you’ll want to exclude the Lease option from consideration and focus on the Borrow option.

Collect Terms

Once you’ve narrowed down your choices to a few cars and figured out which of the Cash, Lease and Borrow options work for you, you will be ready to talk to dealers and other car sellers.  The Inputs tab of the spreadsheet lists all of the information you need for each type of purchase.  I defined each of the inputs earlier in this post.  For every deal you are offered, be sure to get all of these values.  I found that there are some of these values that are consistently unavailable if you look on line.  You may need to ask for some of these items specifically.  If you aren’t sure you are getting straight answers, you can always ask for the actual contract.  It is required to have all of the terms.

Enter Values in Spreadsheet

Next, enter all of the values into the Inputs tab.  Then, go to the tab that corresponds to the time period you plan to own your car – Lease Term or Drive Forever.  You can see the total cost of the options for which you entered the data.

If you have deals for more than one car, I suggest making one copy of the spreadsheet for each car.  You can then compare not only between the Cash, Lease and/or Borrow options for a single car, but can compare whichever options are available to you across cars.

Your final choice of car and deal could be the least expensive or a different one. It will all depend on your personal financial situation, your qualitative considerations and their relative importance.  Buying a car is an important decision, so cost may not be the only factor to influence your decision.

Download Car Comparison Spreadsheet

The Basics of Loans

Loans are the financial instrument people use to borrow money.  Whether they are getting a mortgage to buy a house, borrowing money to buy a car (as opposed to leasing or paying cash as discussed in this post) or other large purchase, not paying off their credit card in full or borrowing money from a friend, they are taking out a loan.  In this post, I will:

  • introduce the key terms
  • describe how loans work
  • identify the factors that determine your monthly payment
  • talk about some common borrowing mistakes

In future posts, I’ll provide more specifics about car loans, mortgages and credit cards.

Key Terms

There are four basic terms common to almost all loans.  They are:

  • Down payment – The amount you have to pay in cash up front for your purchase.  For large purchases, such as homes, condos and vehicles, the lender requires that you pay for part of the purchase immediately.  This amount is the down payment. The lender wants you to have a financial interest in maintaining your purchase so it doesn’t lose value (as in the case of a residence) or lose value more quickly than expected (as in the case of a car).  For some other types of loans, no down payment is needed. Examples of such loans are student loans, credit card balances and personal lines of credit.
  • Principal – The amount you borrow.
  • Interest rate – The percentage that is multiplied by the portion of the principal you haven’t repaid yet to determine the amount of interest you owe.  Interest rates are usually stated as annual percentages. They are divided by 12 to determine the interest that is due each month.
  • Term – The time period over which you re-pay the loan.

Loan Basics

How the Money Moves

When you borrow money, the lender usually pays a third party on your behalf.  For example, when you buy a home or use a credit card, the lender gives the money directly to the seller or its escrow agent.  For some loans, the lender gives the money to you, such as with a line of credit. The amount of money the lender gives you or pays on your behalf is the principal.

You then re-pay the loan by paying the lender periodically (usually monthly or bi-weekly).  For most loans, you start making payments immediately. For some loans, though, such as student loans and some car loans, you don’t have to make payments right away.  Most student loans don’t require any re-payments until after graduation. When entering into a loan that doesn’t require immediate payments, it is critical to understand whether interest will be adding up between the time you enter into the loan and the time you start making payments.  Several years of interest, even at a low rate, can increase the amount you need to re-pay substantially.

Payments Include Principal and Interest

Part of each payment is the interest the lender charges you for letting you use its money.  The rest covers repayment of the principal. For example, if you borrowed $20,000 (the principal) at 5% (the interest rate) and started making monthly payment right away, the lender would calculate the interest portion of your first payment as 5% divided by 12 (months) times $20,000 or $83.33.  Your monthly payment also includes some principal. If you have a 10-year term on this loan, your monthly payment will be $212.13. In this case, you will re-pay $128.80 ($212.13 – $83.33) of principal in the first month.

In the second month, you’ll pay interest on $19,871.20 which is the original $20,000 you borrowed minus the $128.80 of principal you paid in the first month.  Your interest payment will be $82.80 and your principal payment will be $129.33. Every month, you will pay more principal and less interest. The chart below shows the mix of interest and principal in each of the 120 payments of your 10-year loan.

Factors that Determine Your Monthly Payment

The monthly payment on a loan is a function of three numbers:

  • Interest rate – the higher the rate, the higher your monthly payment.
  • Principal – the more you borrow, the higher your monthly payment.
  • Term – the longer the term, the less your monthly payment.

Sensitivity to Interest Rate and Term

The table below shows the monthly payment on a $20,000 loan for a variety of combinations of interest rates and terms.

Term (in years) Interest Rate
3% 5% 7% 9%
5 359 377 396 415
10 193 212 232 253
20 111 132 155 180
30 84 107 133 161

The amount of principal for all of the loans in the table above is $20,000.  Therefore, when the total amount of your payments increases, it is because you are paying more interest.  The table below shows the total amount of interest you would pay for each of the same combinations of interest rates and terms.

Term (in years) Interest Rate
3% 5% 7% 9%
5 1,562 2,645 3,781 4,910
10 3,175 5,456 7,866 10,402
20 6,621 11,678 16,214 23,187
30 10,355 18,651 27,902 37,933

Even with the loans with interest rates as high as 9% have much higher payments and total interest than loans with lower interest rates. The interest rates charged on credit cards are often even higher than 9%. This table shows the importance of avoiding the use of credit card debt and refinancing your credit card debt through another lender if it is very large, if at all possible.

What Determines the Interest Rate?

There are several factors that determine your interest rate.

The Economy

The first is the economic environment. If interest rates, such as those on government bonds, are high, the interest rate you will be charged will be also be high.  The US government is considered to have almost no risk of not re-paying it loans, whereas individuals have varying levels of risk. The higher the risk that a loan won’t be re-paid, the higher the interest rate.  Therefore, most loans to individuals have an interest rate that is higher than the interest rate on a US government note, bill or bond with the same maturity.

Credit Score

Along the same line, your credit score is also an important factor in determining your interest rate.  When you have a higher your credit score, lenders believe the risk you won’t re-pay the loan is lower so they charge you a lower interest rate.  My post on credit scores provides lots of details on how to improve your score.

Collateral

A third factor in determining the interest rate is whether or not you pledge collateral and how much it is worth relative to the amount of the loan.  If you pledge collateral, the lender can take it from you if you fail to make your payments. Examples of loans that automatically have collateral are vehicle loans and mortgages.  On those loans, the lower the ratio of the principal to the value of the collateral, the lower the interest rate. That is, if you make a larger down payment on a particular house, your interest rate is likely to be lower than if you make a smaller down payment.  Examples of loans that don’t have collateral are credit cards and student loans. When there is no collateral, interest rates tend to be higher than when you pledge collateral.

Co-Signers

Another approach for reducing your interest rate is to have someone with a better credit score co-sign your loan.  The co-signer is responsible for making your payments if you don’t. For young people, parents are the most common co-signers.

The Math behind Your Monthly Payment

In this section, I’ll briefly explain the math that determines your monthly payment and will provide a bit of information about the Excel formulas you can use.  Feel free to skip to the next section on common borrowing mistakes if you aren’t interested in this aspect of loans!

Present Values

The fundamental concept underlying the determination of the monthly payment on a loan is that the sum of the present values at the loan interest rate of the monthly payments on the day the loan is issued is equal to the principal.  A present value tells the values today of a stated amount of money you receive in the future. It is calculated by dividing the stated amount of money by 1 + the interest rate adjusted for the length of time between the date the calculation is done and the date the payment will be received.  Specifically, the present value at an interest rate of I of $X received in t years is:

The denominator of (1+i) is raised to the power of t to adjust for the time element.

The present value of all of your loan payments is then:

where t is the number of months until each payment and i is the annual interest rate.

Solving for Your Monthly Payment

This amount is set equal to the principal.  The monthly payment can be calculated using a financial calculator, such as in Excel, or mathematically.  The Excel formula is pmt(i/12, t, X). It will give you the negative of your monthly payment. ipmt and ppmt return the portion of each payment that is interest and principal, respectively.  In month y, the interest is ipmt(i/12, y, t, X).

For those of you who really like math, you can also calculate the monthly payment directly.  If payments were made forever (an infinite series), the sum above would equal X/i. We need to eliminate the infinite series of payments after the end of the loan to determine the present value of the loan payments.  Those payments have a present value of X/i divided by (1+i)term.  If we subtract the present value of the payments after the loan term ends from the present value of the infinite series, we get

That is a bit of a messy formula, but, having gotten rid of the big sum, it can be solved using a fairly basic calculator.

Common Borrowing Mistakes

Some people end up in difficult financial situations, in bankruptcy or even homeless due to poor borrowing decisions.  A few of the more common mistakes are identified below.

Not Understanding the Terms

Many mistakes result from not reading or not understanding the loan agreement.  For example, some loans (mortgages in particular) have teaser rates or adjustable interest rates.  If the interest rate goes up on your existing loan at some point in the future, your payments will also go up.  If you have an adjustable interest rate on a loan, you want to make sure you’ll be able to afford higher payments if interest rates increase.

Another example of a loan provision that can be problematic is a balloon payment.  Under some loans, the monthly payment is calculated as if the loan has a long term, such as 15 or 30 years.  However, after a shorter period of time, say 5 or 10 years, the remainder of the principal must be re-paid and the loan terminates.  If you haven’t built up enough cash to re-pay the principal or can’t get another loan at a rate you can afford, you might default on your loan.

High Cost of Ownership

Many things that people buy with a loan come with other costs that they haven’t considered and might not be able to afford.  For example, when you buy a car, you not only have to make your car payments, but also will need to pay for insurance (including physical damage coverage at a fairly low deductible if required by the lender), gas and maintenance.  Similarly, while you may be able to fit your mortgage payment in your budget, you also need to be able to afford the costs of utilities, homeowners insurance and maintenance. In some cases, these additional costs lead to financial difficulties.

Mistakes that Increase Monthly Payments

Some mistakes cause people to have higher payments than necessary.  For example, if you take out a personal loan from a bank, you often have the option to post collateral.  If you do so, your interest rate is likely to be lower, possibly by as much as 50%.

Another way people end up with monthly payments that are higher than they need to be is to take out a loan that is bigger than necessary.  For example, if you can afford to make a larger down payment than you actually make, the principal on your loan will be higher which increases your monthly payment.  Many loans have pre-payment penalties which make it cost-prohibitive to pre-pay your principal to bring it back in line with the amount you should have borrowed in the first place. Also, if the lower down payment increases the ratio of the principal to the value of your home by too much, it will also increase your interest rate which further increases your payment.

Overestimating the Value of Your Collateral

Another problem people encounter is an inability to borrow as much as they need because they overvalue their collateral.  Common issues that arise include:

  • Lenders get their own appraisals of houses.  The lender’s appraisal is often lower than the purchase price and sometimes even lower than the assessed value.  If the appraisal is less than the purchase price, the buyer must increase his or her down payment so the ratio of the loan to the appraised value is within the lender’s limits.  Even worse, some banks won’t issue the mortgage at all if the difference between the appraisal and the purchase price is too big, even if you increase your down payment. In those situations, you need to either find another lender or re-negotiate your purchase price.
  • Lenders use the National Auto Dealers Association (NADA) Guides to value used cars.  These values can be different from Kelley Blue Book. In particular, the NADA Guides adjust the value based on the specific location of the vehicle.  Also, the values in the NADA guides assume that the vehicle is in pristine condition for its age. If it has had any heavy use at all, the lender will reduce the value before determining the value of the collateral.
  • For used cars, washed titles are also a problem.  When a car has been severely damaged, its title is changed from the more typical “clean” title to a salvage title.  However, when a car’s title is transferred from state to state, its damage history can get sometimes get lost as some states do not require salvage titles.  However, other sources, such as CARFAX, maintain the information about the damage. Lenders will check these other sources before determining the value of the collateral.

While collateral helps reduce the interest rate on your loan, it is important to consider these points in determining the value of your collateral.