# Smart Account Choices Juice Long-Term Growth Compound interest allows your investments to grow exponentially in value.  This post provides six online compound interest calculators to help you understand the benefits of compound interest on the future value of your investments.  Importantly, you can see the impact of income taxes on the ability of your investments to grow.  The six compound interest calculators will cover most of your account types:

1. Basic

Then building in the effects of income taxes on:

2. Appreciation

3. Cash Returns

4. Cash Returns AND Appreciation

5. Final Withdrawal

And finally:

6. Comparisons Across Accounts

You can pick from among these compound interest calculators to find the one(s) that best match your situation.

## Compound Interest Formula

All of the calculators use the basic compound interest formula: The calculators differ in the types of returns and related income taxes.  The Basic Compound Interest Calculator works great if you don’t care about income taxes or you already have your money in a tax-free account.  The next three calculators help you understand the impact of income taxes if you hold your money in a taxable account.  Next, the fifth calculator applies income taxes when the money is withdrawn as happens with a tax-deferred account.

I saved the best calculator for last.  It compares the future value of your after-tax investments based on the type of account in which you hold your assets.

## Using the Calculators

Before going into the details of the calculations, here are a couple of tips:

1. The interest rate should be the effective interest rate.  That is, if interest is paid more frequently than once per period, the interest rate you enter should be the total interest paid in the first period divided by the initial principal.  This calculation allows you to reflect the benefit of compounding when interest is paid more often than once per period.
2. Enter percentages as numbers, not decimals.  For example, enter 50 and not 0.50 for 50%.
3. To move between input fields, you can either click on each field with your mouse or use the tab key to go to the next field or shift-tab to get to the previous field.  The calculator output is the accumulated value of your investment, i.e., your final balance.

## Basic Compound Interest Calculator

The first calculator demonstrates the benefit of the compounding of interest.  Other returns, such as dividends and appreciation, compound in the same way.  In this post, I’ll use compound “interest” to cover all types of returns.

To use this calculator, first input your initial investment (also known as your initial principal or initial balance).  Then input the rate of return (rate of interest) each period and the number of periods. The interest rate should be the return you expect per period.  For example, if your periods are years, then you will enter the annual interest rate.

In these calculators, the portion your return that is distributed in cash, such as dividends or interest, is reinvested at the rate of return you input.

This calculator ignores income taxes on your returns. Alternately, you can think of the implicit income tax rate as being 0%.  As such, the ending balance corresponds to what you would have if you already hold your investments in a tax-free account, such as a Roth retirement account in the US or a tax-free savings account (TFSA) in Canada.

## Calculator with Income Taxes on Appreciation

This calculator applies income taxes using the following assumptions:

• 100% of your returns are in the form of appreciation.
• You sell your investment at the end of the last period.

There is one more input than in the previous calculator – the income tax rate on appreciation. In the US, the tax rate on appreciation for most people is 15% plus your state income tax rate.  In Canada, it is 50% of the tax rate on your wages which, for most people, corresponds to a tax rate on appreciation of 10.25% or 13% plus provincial income tax.

## Calculator with Income Taxes on Cash Returns

The next calculator applies income taxes by assuming that 100% of your returns are in the form of cash distributions, such as dividends or interest.  For this calculator, you will enter the income tax rate on cash returns.  In the US, the tax rate on dividends for most people is 15%.  The US tax rate on interest is the same as the tax rate on your wages which, for many people, is 22% or 24%.  In Canada, the tax rate on both dividends and interest is equal to the tax rate on your wages which, for most people, is 20.5% or 26%.

## Calculator with Income Taxes on Appreciation and Cash Returns

The next compound interest calculator adjusts your ending balance for income taxes on both appreciation and cash returns.  There are two inputs for each of returns and income tax rates – one for each of appreciation and cash distributions.  The sum of the two return percentages should equal your total return estimate.  You enter the returns separately to appropriately reflect the differences in the timing and amounts of income taxes.

## Calculator with Income Taxes Upon Distribution

This calculator adjusts your ending balance for income taxes paid on the entire amount of your investment when it is withdrawn.  The income taxes in this calculator correspond to what you would pay if you withdrew the ending balance from a traditional retirement plan in the US (401(k) or individual retirement account – IRA) or a Registered Retirement Savings Plan (RRSP) in Canada.  This calculator has only one income tax rate.  In both the US and Canada, the tax rate is equal to the marginal rate on your wages and other ordinary income.  As noted above, for many people in the US, 22% and 24% are common ordinary income tax rates and typical ordinary income tax rates are 20.5% and 26% in Canada.

## Comparison Calculator

This last calculator lets you compare your final after-tax balance based on the type of account into which you put your money. The three types of accounts are (1) taxable, (2) tax-deferred and (3) tax-free. The most common tax-deferred accounts in the US are traditional 401(k)s and IRAs.  Canadian RRSPs are also tax-deferred accounts. Roth retirement accounts in the US and TFSAs in Canada are tax-free accounts. This post provides more information about these types of accounts.

The first three inputs relate to the amount you have to invest and your returns, as in the previous calculators.   The remaining four inputs are the tax rates applicable to your:

• Cash distributions.
• Appreciation.
• Ordinary income now.
• Ordinary income when you withdraw money from your tax-deferred account.

For all three types of accounts, the calculator assumes that you earned the money you invest during the calendar year in which it is first invested.  As such, income taxes (at your ordinary income tax rate today) are deducted from your initial account balance if you put the money in a taxable or tax-free account.  There is no up-front income tax if you put the money in a tax-deferred account.

In all three accounts, the amount invested equals the initial amount you enter minus any up-front income taxes.  Periodic income taxes are calculated using the Calculator with Income Taxes on Appreciation and Cash Returns if you put your money in a taxable account.  The Calculator with Income Taxes Upon Distribution is used for tax-deferred accounts, using the estimate of your ordinary income tax rate when you retire.   There are no additional income taxes (i.e., other than the up-front taxes) for money put in a tax-free account.

This calculator illustrates the concepts discussed in these posts on tax-efficient investing in the US and Canada.