# 6 Compound Interest & Simple Interest Examples (w/ Formulas!)

Whether you’re saving money for a down payment on your house or you want to make sure you have money to use in an emergency, compound interest is your friend. While simple interest earns you money only on the amount you deposit, compound interest is your interest earning interest – and that means your savings grows more quickly!

We recognize that, for some of our Addition Financial members (and prospective members), it may be difficult to visualize what a big difference compound interest can make in your savings. We also know that you may not know how to calculate compound interest to maximize your earning potential. In this post, we’ll share six compound interest examples and simple interest examples, along with the formulas you can use to compare accounts and put your money to work for you.

We will break the formulas down step by step, but the easiest way to do them is to use a calculator. If you simply enter the formula exactly as we list it using your numbers and rates, you will get accurate results.

## Example #1: Calculating Simple Interest

Let’s start by looking at how to calculate simple interest. Imagine that Sam receives a \$10,000 gift from his grandmother. He puts the money into a traditional savings account with simple interest at an annual interest rate of 0.5% and he wants to know what will happen if he leaves the money there for two years without touching it or adding to it.

Here is the simple interest formula:

### I = P x r x t

In this formula, I stands for interest amount, P stands for principal balance, r stands for the interest rate expressed in a decimal form, and t stands for time. The numeric simple interest formula for our example with Sam would be:

### I = \$10,000 x 0.005 x 2

The total amount of simple interest Sam would earn on his \$10,000 in two years is \$100. As the name suggests, this is a simple equation and a very straightforward one.

## Example #2: Calculating Total Account Balance with Simple Interest

What if Sam wanted to know (without stopping to calculate the interest alone) what his total account balance would be at the end of five years? In that case, he would use a different formula that would give him the total.

### A = P(1 + rt)

In this formula, A stands for the total accrued amount, P is for principal amount, r is for the interest rate expressed in a decimal form, and t is for the time in months or years. To calculate Sam’s balance after five years, the numerical formula would be as follows.

### A = \$10,000(1 + 0.005*5)

In this formula, you would calculate the rt part of the formula first, so the total interest earned for the period would be 0.025. Then, you would multiply the principle by 1 + 0.025, or 1.025, for a new total balance at the end of five years of \$10,250.

## Example #3: Calculating Rate of Interest per Compounding Period, Simple Formula

Now, let’s explore what happens if Sam makes an initial deposit of \$10,000 into an account that compounds interest, such as an insured money market account. If he wanted to know how much interest he was earning in each compounding period, he could calculate that by taking his current balance and using this formula.

### r = (A/P)1/t - 1

In this formula, r stands for the actual interest rate expressed as a decimal, A is the accrued amount, P is the principal amount, and t is the number of compounding periods. So, numerically speaking, the formula would look like this.

### r = (\$11,200/\$10,000)1/36 - 1

For this formula, we have assumed that Sam’s new balance is \$11,200 and he has interest that compounds monthly. The money has been in the account for three years. You’ll use the formula by first, dividing the accrued amount (A) by the principal amount (P) to get 1.12. Then you would divide 1 by 36 to get the correct exponent of 0.0278. The result is that he is earning 0.315 % interest in each compounding period.

The thing we hope you’ll take away from this formula and all others related to compound interest is what a big difference compounding interest can make in your savings. If Sam had put his money into an account with simple interest at the same annual rate, his ending balance after three years would be \$11,134. With compound interest, he earned an additional \$66 in that time. With a higher balance, the compound growth would be even bigger – and would only grow larger over time. ## Example #4: Calculating Potential Earnings Based on Annual Rate

Anybody who wants to put their money into a compound interest account should know how to compare accounts. If Sam wanted to be sure to pick the account that would help him earn the largest possible amount of interest, he would need to calculate how much money he would earn in various accounts. The best way to do that is to calculate potential earnings based on the annual rate and compounding periods. Of course, there’s a formula that will allow you to do that.

### A = P(1 + r/n)nt

In this compound interest formula, A is the accrued amount at the end of a period, P is the principal amount, r is the annual percentage rate as a decimal, n is the number of compounding periods per unit of time, and t is the time. Let’s look at how this would play out with Sam’s \$10,000 if he wanted to know how much he would earn after 1 year of daily compounding with a 5% annual interest rate.

### A = \$10,000(1+.05/365)365

The first step here would be to divide the interest rate by the number of accrual periods. 0.05 divided by 365 is 0.000136986.

Add 1 and multiply that number (1.000136986) by the principal to get \$10,001.000136986. Then, raise that number to the exponent of 365.

The result is that Sam would have a new balance of \$10,512,67. If you compare that to an account with simple interest at the same annual rate, Sam would have earned 5% per year for a total of \$10,500 after one year.

## Example #5: Calculating APY Based on an Annual Rate

Terms related to interest can be confusing. When you’re comparing accounts, you’ll need to be careful to do an apples-to-apples comparison. Let’s say that Sam is trying to compare compound interest accounts and one account provider gives him an annual percentage rate and the other gives him an annual percentage yield (APY). He will need to convert the annual rate to an APY to compare them. Here is the APY formula.

### APY= (1 + r/n )n – 1

As in the other formulas, r stands for the annual percentage rate as a decimal, and n is the number of accrual periods. For this example, we’ll use a 5% interest rate and weekly accrual. The numbers look like this:

### APY = (1 + .05/52)52 - 1

Divide 0.05 by 52 and add 1 to get 1.000961538. Raise that number to the power of 52 and add 1 to get 0.0512458. When you convert that to a percentage, you’ll see that the annual percentage yield is 5.12458%. If Sam were comparing this account to one with an APY of 5%, he would be best served by choosing this account because it would earn him more interest.

## Example #6: Building Wealth with Compound Interest

For our final formula, we want to illustrate just how powerful compound interest can be over time. Imagine that Sam received \$100,000 instead of \$10,000. If he was 20 years old when he received that money and he left it in a money market account with a 5% interest rate compounded daily, how much would he have by the time he’s reached the age of 50?

As a reminder, the compound interest formula to calculate potential earnings is A = P(1 + r/n)nt. With Sam’s new numbers, the formula would be:

### A = \$100,000(1 +.05/365)365*30

The result may be surprising to you. While the annual growth rate difference between a compound and simple interest rate is small, Sam’s balance after 30 years would be \$448,122.89. With simple interest, he would have earned \$150,000 in accrued interest for an ending balance of only \$250,000. That means he would earn 2.32 times as much interest with compound interest.

We saved this example for last because it illustrates exactly how important compound interest is if you want to save for your retirement. Even if you don’t invest in the stock market or take big risks, you can accumulate a lot of money if you choose a compound savings account and leave your money there, so it can grow.

We recognize that crunching numbers to compare accounts doesn’t come easily to everyone. We hope that the formulas we have included here will help to demystify the math and help you to choose the best accounts to help you achieve your financial goals.