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 $638 per month, and you have 36 months left on your loan. If you pay an additional $1,300 with your next regular $638 payment (due in one month), how much will it reduce the amount of time left to pay off your loan? (Be careful not to round any intermediate steps less than 6 decimal places.)

Answer 1

Solution

EMI = P* r*[( (1+r)ⁿ ) / ((1+r)ⁿ - 1 )]

P = principal amount

r = rate

n = no. of installments

Here ,

EMI = 638

r= 6.7% / 12 = 0.558333%

n = 36 months

Applying values,

638 = P * 0.558333% [(1.00558333)³⁶ / (1.00558333)³⁶ - 1 )]

638 = P * 0.558333% [ 5.505696]

115.879999 = P * 0.558333%

P = $20754.62675

Repayment schedule is attached below with principal amount calculated above.

Hence as per the schedule, the loan gets repaid in 34 months, ie, 2 months earlier.