Question

A loan is repaid by making payments of $2000.00 at the end of every six months for twelve years. If interest on the loan is 10% compounded quarterly, what was the principal of the loan?

Answer 1

Periodic 6 monthly payment for the loan = $2,000

Interest rate = 10% compounded quarterly

Calculating semi-annual interest rate from Quartery compounded rate:-

where, r = Interest rate = 0.10

m = no of times compounding in a year = 4 (Quarterly compounding)

n = no of periods for semi-annual rate = 2

Rate = 5.0625%

Now, Calculating the Principal Loan amount:-

where, P = Loan Amount

r = periodic Interest rate = 5.0625%

n = no of periods = 12 years*2 = 24

P = $27,430.28

So, Prinncipal Loan Amount is $27,430.28