Question

Alysha would like to borrow $31,000 to pay one year’s tuition at a private U.S. university. She would like to make quarterly payments and finish repaying the loan in 5 years. If the bank is quoting her a rate of 6 percent compounded monthly, determine her quarterly payment.

(Round effective interest rate to 4 decimal places, e.g. 25.1253% and final answer to 2 decimal places, e.g. 125.12.)

Answer 1

Amount borrowed by Alysha = $31,0000

Interest rate quoted by bank is 6% compounded monthly

First we will convert monthly compounding into Periodic Quarterly Rate,

Periodic Quarterly Rate = (1+Monthly Rate)^n - 1

where, Monthly Rate = 6%/12 = 0.5%

n = no of months in a quarter = 3

Periodic Quarterly Rate = (1+0.005)^3 - 1

Periodic Quarterly Rate = 1.5075%

Now, Calculating the Quarterly payments agianst the mortgage:-

Where, P = Loan amount = $31,000

r = Periodic Quarterly rate = 1.5075%

n= no of periods = 5 years*4 = 20

Quarterly payments = $1806.95

So, Alysha's quarterly payment is $1806.95