A commercial bank will loan you 30981 for 8 years to buy a c

A commercial bank will loan you $30,981 for 8 years to buy a car. The loan must be paid in equal monthly payments at the end of the month. The annual interest rate on the loan is 16.41 percent of the unpaid balance. What is the amount of the monthly payments?

Solution

Solution:

Loan amount = $30,981

Period = 8 years

Annual interest rate = 16.41%, monthly interest rate = 16.41/12 = 1.3675%

Loan is to be paid in equal month installment, therefore loan will be repaid in 96 (8*12) installments. Let a is the monthly installment of loan.

Therefore present value of loan installment at 1.3675% for 96 periods will be equal to amount of loan.

Hence

a * Cumulative PV factor at 1.3675% for 96 periods = $30,981

a * 53.27461031 = $30981, a = $581.53

Hence amount of monthly payments will be $581.53