Problem 1
If you have a bank account whose principal = $1,000, and your bank compounds the interest twice a year at an interest rate of 5%, how much money do you have in your account at the year's end?
Compound interest is a great thing when you are earning it! Compound interest is when a bank pays interest on both the principal (the original amount of money)and the interest an account has already earned.
To calculate compound interest use the formula below. In the formula, A represents the final amount in the account after t years compounded 'n' times at interest rate 'r' with starting amount 'p' .
This page focuses on understanding the formula for compound interest ; if you're interested in taking a deeper dive into how compound interest works and exploring some real world examples, please read our article here.
Practice Problems
Problem 2
If you start a bank account with $10,000 and your bank compounds the interest quarterly at an interest rate of 8%, how much money do you have at the year's end? (assume that you do not add or withdraw any money from the account)
Problem 3
The first credit card that you got charges 12.49% interest to its customers and compounds that interest monthly. Within one day of getting your first credit card, you max out the credit limit by spending $1,200.00. If you do not buy anything else on the card and you do not make any payments, how much money would you owe the company after 6 months?
Note: since the duration of time is half of a year, the value of t is ½.
6 months is half of a year, and t in the compound interest formula is measured in years.
Problem 4
You win the lottery and get $1,000,000. You decide that you want to invest all of the money in a savings account. However, your bank has two different plans.
Plan 1
The bank gives you a 6% interest rate and compounds the interest each month.
Plan 2
The bank gives you a 12% interest rate and compounds the interest every 2 months.
Question: In 5 years from now, which plan will provide you with more money.
Further Reading
