# Compound Interest Calculator

Use this calculator to see how quickly your money grows from compound interest. With options to choose how often interest is compounded, length of time saved, along with initial starting amount and regular monthly deposits, this compound interest calculator shows the power of compounding during each period and why saving and investing early is important.

 Starting Amount: \$ Interest Rate: % Length of Time: yearsmonths Additional Contributions: \$ per month Compound Interval: DailyMonthlyQuarterlyBiannuallyYearly

## What Is Compound Interest?

Compound interest is the addition of interest to the principal amount or starting deposit so that the interest earned in the next period is the sum of the previous period’s amount plus the accumulated interest. Compound interest can be thought of as earning interest on interest. Unlike simple interest, which is calculated only on the principal amount, the balance from compound interest grows at an increasing rate over time.

For example, if \$100 was deposited into a savings account paying 10% interest a year. At the end of the first year, the balance in the account will be \$110. After the second year the account will have \$121. In the end of the third year, the account will have \$133.

Thanks to the power of compound interest, a few dollars today can turn into big money over the course of a lifetime.

## What Is The Formula For Compound Interest?

The formula to calculate compound interest is: A = P(1+ r/n)nt

A = amount of money accumulated, including interest
P = principal or initial starting amount
r = annual interest rate as a decimal
n = number of times the interest is compounded per year
t = the number of years the amount is invested or borrowed

Example:

An amount of \$5000 is deposited into a bank savings account paying an annual interest rate of 4.5% compounded quarterly. What is the balance after 7 years?

Solution:

A = 5000(1 + .045/4)4(7)
A = 5000(1.01125)28
A = 5000(1.36785156)
A = 6839.26

The amount in the account after 7 years will be \$6,829.26.

## How Do Compounding Periods Affect Interest Received?

When calculating compound interest, the number of compounding periods matter. When interest is compounded daily, month, quarterly, semi-annually, or annually, the more frequent the compounding period, the greater the amount of interest is earned.

The below table shows the ending balance of the different compounding periods when \$10,000 is invested with an annual interest rate of 10% over 10 years:

 Compounding Frequency Compounding Periods (n) Interest Per Period (r/n) Years Invested (t) Ending Balance Annually 1 0.10 10 \$25,937.42 Semi-Annually 2 0.05 10 \$26,532.98 Quarterly 4 0.025 10 \$26,850.64 Monthly 12 0.008333 10 \$27,070.41 Daily 365 0.000274 10 \$27,179.10

## What Is The Compound Rule of 72?

A quick and easy way to calculate the number of years to double one’s money in an investment is to use the rule of 72. Dividing 72 by the interest rate gives a rough estimate of the number of years for an investment to double.

For example, at a 8% annual interest rate, 72 divided by 8 equals 9 years.