Question 256017
Luis borrowed $125,700.00


during his 3 years of school, the loan amount increased to $132,110.70.


he has to pay back this loan in 10 years at 3.2% interest per year compounded monthly.


what are the monthly payments?


the formula you will want to use is the payment for a present value formula.


that formula is:


{{{ PMT(PV) = (PV / ((((1 - (1 / ((1+i)^n))))/i))) }}}


PMT = Payment per Time Period	
PV = Present Value
i = Interest Rate per Time Period
n = Number of Time Periods


PV = Present Value = $132,110.70 which the amount of the loan that has to be paid back.


i = interest rate per time period = 3.2% / 100% = .032 / 12 = .0026666667


n = number of time periods = 10 years * 12 = 120 months.


your formula becomes:


{{{ PMT(PV) = (132110.70 / ((((1 - (1 / ((1.002666667)^120))))/.002666667))) }}}


this becomes:


PMT(PV) = 1287.903449.


monthly payments are 1287.903449 = $1,287.90


to confirm this answer is correct, you can plug it into the present value of a payment formula shown below:


{{{ PV(PMT) = (PMT * (1 - (1 / (1+i)^n))/i) }}}


PV = present value
PMT = payment per time period
i = interest rate per time period
n = number of time periods


PMT = 1287.903449
i = 3.2% / 100% = .032 / 12 = .0026666667 per month.
n = 10 * 12 months per year = 120 months.


formula becomes:


{{{ PV(PMT) = (1287.903449 * (1 - (1 / (1.0026666667)^120))/.0026666667) }}}


this becomes:


PV(PMT) = 132110.7


since this is what we started out with, the formula is good and the answer is:


your monthly payments are $1287.90.