Question

You want to buy a car, and a local bank will lend you $20,000. The loan will be paid off over 5 years with equal monthly payment.

a) If the nominal interest rate of the loan is quoted as 6% with monthly compounding assumption, what is your monthly payment?

b)What is the effective annual rate of Part(1)?

c) If the nominal interest rate of the loan is quoted as 6% with semiannual compounding assumption, what is your monthly payment?

Answer 1

a) rate per month  = 6%/12 = 0.5%
PMT = 20,000*(1-(1+0.5%)^-5*12)/0.5% = 386.66

b)Effective rate = (1+6%/12)^12-1 = 6.17%

c) EAR = (1+6%/2)² -1 = 6.090%
PMT = 20,000*(1-(1+6.090%/12)^-5*12)/6.090%/12 = 387.49