Question

You have some extra cash this month and you are considering putting it toward your car loan. Your interest rate is 7.5%​, your loan payments are $629 per​ month, and you have 36 months left on your loan. If you pay an additional $1,400 with your next regular $629 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

PV of Loan amount = PMT*(1-(1+r)^-n)/r =629*(1-(1+7.5%/12)^-36)/(7.5%/12) = 20,221.037374

New PMT = 629+1400 = 2029

So to find new time period
PV of Loan amount = PMT*(1-(1+r)^-n)/r
20,221.037374 = 2029*(1-(1+7.5%/12)^-n)/(7.5%/12)
20,221.037374*7.5%/(12*2029) = 1 -1.00625^-n
0.0622876 = 1 -1.00625^-n
1.00625^-n = 1-0.0622876
applying log on both sides we get
n = 10.32
The reduction in months = 36-10.32 = 25.68 months

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