The new time left to pay off your loan will be _ months? Thus, you reduce the amount of time remaining on the loan by approximately _ months?

Question

 You have some extra cash this month and you are considering putting it toward your car loan. Your interest rate is

6.7%​,

your loan payments are

$606

per​ month, and you have

36

months left on your loan. If you pay an additional

$1,400

with your next regular

$606

payment​ (due in one​ month), how much will it reduce the amount of time left to pay off your​ loan? ​(Note: Be careful not to round any intermediate steps less than 6 decimal​ places.)

Answer 1

Step 1. Calculate the present value of your future payments in the next month (using the financial calculator):

N = 35, I/Y = 6.7% / 12 = 0.558%, PMT = 606, FV = 0, CPT PV = 19,218.831380

Step 2. Since you pay 1,400 more next month, the present value calculated in Step 1 will be reduced by 1,400 to 17,818.831380. Using the new present value, you can get the number of months of your future payments.

PV = -17,818.831380, PMT = 606, I/Y = 0.558%, FV = 0, CPT N ≅ 32

So the new time left to pay off your loan will be 32 months? Thus, you reduce the amount of time remaining on the loan by approximately 3 (=35 - 32) months.