You have some extra cash this month and you are considering putting it toward your car loan. your interest rate is 6.6%, your loan payments are $664 per month, and you have 36 months left on your loan. if you pay an additional $1,100 with your next regular $664 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.)

Number of payments will drop from 36 months to 34 months

Explanation: Firstly you need to calculate the current loan amount's balance, i.e. the present value of the loan:

Using a financial calculator

N = number of months

I/YR = interest rate per month

FV = final value - the value at the end of the period

PMT = Payment per month

PV = Present value - current value of the loan

N = 36 months

I/YR = 6.6% ÷ 12 months = 0.55% per month

FV = 0 (value when loan is completely paid off is 0)

PMT = $664

∴ PV = $21632.5122

However you have an extra $1,100 to pay towards your loan. Therefore the new balance is $21632.5122 - $1,100 = $20532.5122

Using this new balance as the PV, the number of months will be affected. So you need to recalculate how many months it would take to pay off the balance:

I/YR = 0.55

PV = - $20532.5122 (Punch in as a negative and PMT as positive to compute the correct value)

PMT = $664

FV = 0

∴N = 33.9873 months

Rounded off to 34 months

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