Compound Interest

What is Compound Interest? Interest is money paid for the use of money. It’s generally money that you get for putting your funds in a bank or extra money that must be paid back when you take out a loan. Compound interest is a form of interest where money generated through interest generates even more interest.

Terms Principal: The amount of money that you start with. Interest Rate: The yearly increase in the amount. This is often expressed as a percentage. A 5% interest rate, for instance, means that if interest is added once a year, 5% of the principal will be added to the total amount when interest is calculated.

Number of Times Compounded Interest rates are generally expressed in yearly terms – a 5% interest rate means that the principal will increase about 5% each year. The actual change each year depends on how many times per year interest is added. Say that you have a 5% interest rate and $10,000. If interest is added once a year, you’ll end the year with $10,500. If instead you add 2.5% twice a year, you’ll end up with $10,506. This is because the interest that you get the first time generates extra interest the second time! The more times each year you add (compound) the interest, the more money you end up with.

Calculating Compound Interest

Understanding the Formula

Sample Problem Lucy takes out an unsubsidized loan to help pay for college. When she begins school, she has $25,000 in loans. How much will she have to pay back after 4 years of school, if the interest rate is 3.4% and the interest is compounded every month?

Solution

Sample Problem Bill and Ted each put $20,000 in a retirement savings account, which generates interest at a yearly rate of 1.5%. Bill’s interest is compounded daily, while Ted’s interest is compounded weekly. After 40 years, how much more money will Bill have than Ted?

Solution