Question

**financial management**

You have some extra cash this month and you are considering putting it toward your car loan. Your interest rate is 7.3%​, your loan payments are $669 per​ month, and you have 36 months left on your loan. If you pay an additional $1,400 with your next regular $669 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

Number of Periods = 36
Payment per month = 669
Rate per month = PMT*(1-(1+r)^-n )/r = 669*(1-(1+7.3%/12)^-36 )/(7.3%/12) = 21570.59

The total payment with an additional 1400 with your regular 669 payment = 1400+669 = 2069
PV = PMT*(1-(1+r)^-n )/r
21570.59 = 2069*(1-(1+7.3%/12)^-n)/(7.3%/12)
21570.59*7.3%/(12*2069) = 1- (1+7.3%/12)^-n
0.063422 = 1 - (1+7.3%/12)^-n
applying log on both sides we get
n = - log(1-0.063422)/log(1+7.3%/12) = 10.80 months

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