Loading [MathJax]/jax/output/HTML-CSS/fonts/TeX/fontdata.js

Compound Interest Formula

Compound interest is interest that is calculated on both the money deposited and the interest earned from that deposit.

The formula for compound interest is A=P(1+rn)nt, where A represents the final balance after the interest has been calculated for the time, t, in years, on a principal amount, P, at an annual interest rate, r. The number of times in the year that the interest is compounded is n.

Example 1:

Jasmine deposits $520 into a savings account that has a 3.5% interest rate compounded monthly. What will be the balance of Jasmine’s savings account after two years?

To find the balance after two years, A, we need to use the formula, A=P(1+rn)nt. The principal, P, in this situation is the amount Jasmine used to start her account, $520. The rate, r, as stated in the problem, is 3.5% (or 0.035 as a decimal) and compounded monthly, so n=12. Since we are looking for the balance of the account after two years, 2, is the time, t.

A=520(1+0.03512)12(2)
A=557.65

The balance of Jasmine’s account after 2 years is $557.65.

Example 2:

Lex has $1,780.80 in his savings account that he opened 6 years ago. His account has an annual interest rate of 6.8% compounded annually. How much money did Lex use to open his savings account?

To find the principal, P we can use the same formula, A=P(1+rn)nt. We have the balance of the account, A, after 6 years, which is $1,780.80. The interest rate, r, is 6.8% (or 0.068 as a decimal) and is compounded annually, so n=1. The time, t, is 6, since we know he opened his account 6 years ago. Plug in the known values into the formula and solve for the missing variable, P.

1,780.80=P(1+0.0681)1(6)
1,780.80=1.484P
1,200=P

The principal amount Lex used to open his account 6 years ago is $1,200.

Click here for 20% off of Mometrix Math College Readiness Online Course. Use code: IMCR20

Compound Interest Sample Questions

Question #1:

 
A teacher wants to invest $30,000 into an account that compounds annually. The interest rate at this bank is 1.8%. How much money will be in the account after 6 years?

$43,389.35
$35,389.35
$33,389.35
$37,389.35
Question #2:

 
An investment earns 3% each year and is compounded monthly. Calculate the total value after 6 years from an initial investment of $5,000.

$5,114.74
$4,984.74
$5,984.74
$2,984.74
Question #3:

 
Kristen wants to have $2,000,000 for retirement in 45 years. She invests in a mutual fund and pays 8.5% each year, compounded quarterly. How much should she deposit into the mutual fund initially?

$47,421.08
$35,421.08
$43,421.08
$45,421.08
Question #4:

 
Sean invests $50,000 into an index annuity that averages 6.5% per year, compounded semi-annually. After 9 years how much will be in his account?

$88,918.29
$89,918.29
$68,918.29
$81,918.29
Question #5:

 
Calculate the interest rate for an account that started with $5,000 and now has $13,000 and has been compounded annually for the past 12 years.

9.288%
11.288%
3.288%
8.288%

 

by Mometrix Test Preparation | Last Updated: November 7, 2024