Question

Noah wants to put $1,000 in a savings account with a 1.5% annual interest rate. How much more money will he have after one year if it is compounded monthly versus no compounding?

Answer 1

There are two types of interest: Simple interest and compounding interest:

Simple interest: F = P(1+in)
Compounding interest: F = P(1+i)ⁿ

The compounding interest is always bigger than simple interest for a given amount of n time. The effective interest rate is

Effective interest rate = 1.5%/year * 1 yr/12 months = 0.125% per month

Since there are 12 months in 1 year, n= 12. Then i = 0.125/100 = 0.00125

Difference = Compounded Interest - Simple Interest
Difference = P(1+i)ⁿ - P(1+in) = 1000(1+0.00125)¹² - 1000(1+0.00125*12)
Difference = $0.104

You will only have $0.104 more money than the simple interest.