Question

Car loan interest rate is 7%
loan payment $600 month
36 months left on loan

If pay an addition $1000 with next regular $600 payment (due in a month), how much will it reduce the amount of time left to pay off the loan?

Answer 1

present value of remaining balance
= 600( 1 - 1.00583333^-36)/.00583333
= $19,431.88

you are paying an extra $1000
leaving a present value balance of $18,431.88

so ...
600( 1 - 1.00583333^-n)/.005833333 = 18431.88
1 - 1.005833333^-n = .179198811
1.00583333^-n = .820801188
log it

-n log1.00583333 =log .82080...
-n = -33.95
n = appr 34

So the time would be reduced by 2 months

check:
present value of 34 payments of 600
= 600( 1 + 1.00583333^-34)/.00583333
= 18455.74 , close to $18431 , remember we rounded off the 33.95 to 34