Question

Jerry can purchase a car today costing $76,500 by paying a $20,000 deposit and making no payments for twelve months. Jerry must make his first payment exactly thirteen months from now and continue for a total of 48 monthly payments. Calculate the size of each payment if interest is charged at 6% p.a. compounding monthly.

Answer 1

Car Purchase amount = $76,500

Down payment = $20000

Loan amount = $76,500 - $20,000 = $56,500

years = 5 years from today

n = 48 installment starting after 12 months

2 alternative

Alternative 1 solving by Nominal rate i.e. 6%

Loan amount after 12 month = 56,500 (1+ (6%/12)^12

= 56,500 x 1.0616778

= $59985

Monthly installment = $1408.75

alternative 2 solving by effective rate i.e. = (1+(6%/12))^12 - 1 = 6.17%

Loan amount after 12 month = 56,500 (1+ (6.17%/12)^12

= 56,500 x 1.063475

= $60,086