Question

Alex just took out a personal loan of $34,000. To repay the loan, he has to make equal quarterly repayments for 9 years to the bank. The bank charges an annual percentage rate (APR) of 9% compounded quarterly. How large must each of the quarterly payments be?.

Answer 1

Formula for EMI can be used to compute amount of quarterly payments as:

EMI = P x r x (1+r) n/(1+r) n – 1

P = Principal of loan = $ 34,000

r = Rate per period = 0.09/4 = 0.0225 p. q.

n = Number of periods = 9 years x 4 periods = 36 periods

Quarterly payment = $ 34,000 x 0.0225 x (1+ 0.0225)36/ [(1+ 0.0225)36-1]

       = $ 34,000 x 0.0225 x (1.0225)36/ [(1.0225)36-1]

       = $ 34,000 x 0.0225 x 2.22781641944677/ [(2.22781641944677-1)]

       = $ 34,000 x 0.0225 x 2.22781641944677/ 1.22781641944677

       = $ 1,704.27956087678/ 1.22781641944677

       = $ 1,388.05731368594 or $ 1,388.06

Each quarterly payment will be of $ 1,388.06