Interest is a form of payment from you to your bank, or from the bank to you, based on a principal balance. For example, when you put money in a savings account, you receive payment from the bank for letting them borrow your money. Likewise, when you take out a loan from the bank, you pay money to the bank in addition to the amount you borrowed. This is called interest. Interest is a percentage, and therefore one way to calculate interest is by using the growth factor.
The formula below looks very similar to the one for growth factor, and it is. You can think of as an old value, and as a new value. The growth factor is the same, but there is also an exponent, which tells you how many time units the calculation covers. Here you’ll only look at one time unit.
Formula
Interest calculations
where is the initial balance, and is the interest rate. After periods (or number of times the interest is added) the new balance is .
Example 1
Interest in one time period
You put in a savings account and receive a fixed interest of per year. How much money do you have in the bank after 1 year?
After 1 year you have $ in the bank.
Example 2
Interest in one time period
You’re going to borrow from the bank to finance your graduation party. The bank thinks this is a bad use of the money, and charges an interest rate of . How much do you have to pay back to the bank after 1 year?
After 1 year you have to pay $ back to the bank. Notice that the bank is concerned you won’t be able to pay the loan back, so they are charging you
in interest!
Example 3
Interest in one time period
Last year you put into a savings account. This year you have in the account. What’s the interest on the savings account?
The starting balance is , the final balance is , and the number of time periods is as only one year has passed. Now you just have to insert these figures right into the formula, and solve for :
The interest on the savings account is therefore %.
