Answer to Question #122756 in Financial Math for ashmita

Question

John bought a car worth $29,000 by taking a bank loan. He pays $5,000 initial deposit and agrees to pay $600 at the beginning of each month as long as necessary. What is the number of full payments he needs to make if interest is J12 = 12%?

Answer 1

Amount = $29,000

Initial deposit = $5,000

PMT = $600 beginning of each month

J12 = 12% / 12 = 1% per month

Balance = Amount – Deposit

Balance = $29,000 - $5,000 = $24,000

PMT = $600

FV = PMT * (1+r) (1 – (1+r)^-n)/r

24,000 = 600 * (1+0.01) (1- (1+0.01)^-n)/0.12

24,000/5,000 = (1- (1.01)^-n)*1.01

1- 1.01^-n =1- 4.752475

1.01^-n = -3.75248

-n log 1.12 = -log 3.75248

n = log 3.75248/log1.01

n = 0.574318/0.004321

n = 132.9132 months ~ 133 payments