Question

You have some extra cash this month and you are considering putting it towards your car loan. Your interest rate is 7%, your loan payments are $600 per month, and you have 36 months left on your loan. If you pay an additional $1000 with your next regular $600 payment (due in one month), how much will it reduce the amount of time left to pay off your loan.

Answer 1

Assumption:

I) 7 % is nominal interest rate per anum.

ii) Effective inerest / month is = 0.07 / 12 = 0.583 %

If we take present value today with payment of $600 for next 36 months we will gaet

PV = 600 x (1 - (.00583)^-36) / .00583 = 19431.88

If payments will be increase to 1600 / month, then loan will be repaied earlier than before and repayment wil be in x months hence,

19431.88 = 1600 x (1 - (.00583)^-x) / .00583

Solving x, we will get x = 12.63 months.

Hence, prepayment will be done by 23 months & 11 days earlier ( Considering 1 month = 30 days)

In Xcel - We can find PV with PV function i = 0.582 %, PMT = 600 , Nper = 36

THen setting the PV of 19431.88 with goal seek by changing nper , we will get 12.63.