Car loan: 5-yr annual-payment loan with interest rate of 6% per year.

Question

Annual payment = $5,000.
You have just made a payment and decided to pay the loan off by repaying the outstanding balance.

a) what is payoff amount if you have owned the car for one year (so there are 4 years left on the loan)?

b) What is payoff amount if you have owned the car for 4 years (so there is one year left on the loan)?

please help. thank you.

Answer 1

annual payments on a car loan?
Never heard of that, but, anyway.....

Cash value of car = 5000( 1 - 1.06)^-5)/.06
= 21061.82
a)
value of loan after 1 year had you made no payments at all
= 21061.82(1.06) = 22325.53
but you just made a payment of 5000
So balance after one year = 22325.53 - 5000
= 17325.53

b)
value of loan after 4 years had you made no payments at all
= 21061.82(1.06)^4
= 26590.06
amount of 4 payments
= 5000( 1.06^4 - 1)/.06
= 21873.08
balance after 4 years
=26590.06 - 21873.08
= 4716.98

check: interest on that last balance
= 4716.98(.06) = 283.02
last payment = 4716.98+ 283.02 = 4999.998
not bad eh??