Interest Over One Period

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 K0 as an old value, and Kn 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.


Interest calculations

Kn = K0 (1 + p 100) n

where K0 is the initial balance, and p is the interest rate. After n periods (or number of times the interest is added) the new balance is Kn.

Example 1

Interest in one time period

You put $10000 in a savings account and receive a fixed interest of 4% per year. How much money do you have in the bank after 1 year?

K1 = 10000 (1 + 4 100) 1 = 10000 1.04 = 10400 After 1 year you have $10400 in the bank.

Example 2

Interest in one time period

You’re going to borrow $5000 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 40%. How much do you have to pay back to the bank after 1 year?

K1 = 5000 (1 + 40 100) 1 = 5000 1.40 = 7000 After 1 year you have to pay $7000 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
$7000 $5000 = $2000

in interest!

Example 3

Interest in one time period

Last year you put $2000 into a savings account. This year you have $2100 in the account. What’s the interest on the savings account?

The starting balance is K0 = 2000, the final balance is K1 = 2100, and the number of time periods is n = 1 as only one year has passed. Now you just have to insert these figures right into the formula, and solve for p:

K1 = K0 (1 + p 100) 1 2100 = 2000 (1 + p 100) | ÷ 2000 1.05 = (1 + p 100) 0.05 = p 100 | 100 5 = p p = 5

The interest on the savings account is therefore 5 %.

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