Question

You have 2 different savings accounts. For Account​ A, the simple interest earned after 9 months is ​$6.75. For Account​ B, the simple interest earned after 21 months is ​$19.25. If the interest rate is ​3.6% for Account A and 2.2​% for Account​ B, how much is the principal in each​ account? Which account earned you the most interest the first​ month? Explain your answer.

Answer 1

Account A Principal: $250

Account B Principal : $500

Account B earned $0.17 more interest in the first month

Explanation:

Let the principal in account A be PA and the principal in account B be PB

Simple interest I = Prt where P is principal, r is interest rate (in decimal) and t - time in years

Therefore, given interest I
P = I/rt

We will assume both interest rates are annual interest rates

For account A, interest = 3.6% per year
This works out to 0.036 per year

For account B, interest = 2.2% which works out to 2.2/100 per year = 0.022 per year

Account A
I = 6.75, r = 0.036 t = 9 months = 9/12 year = 3/4 year = 0.75 year

PA = 6.75/(0.036 x 0.75) = $ 250.00

Account B

I = 19,25, r = 0.022, t = 21/12 = 1.75 years

PB = 19.25/(0.022 x 1.75) = P = $ 500.00

Account A interest earned per month = 6.75/9 = $0.75

Account B interest earned per month = 19.25/21 = $0.92

Hence account B earned more interest in the first month
The amount of interest earned by account B over account A
= 0.92 = 0.75 = $0.17