Question

Suppose a graduate student receives a non-subsidized student loan of $12,000 for each of the 4 years the student pursues a PhD. If the annual interest rate is 4% and the student has a 10-year repayment program, what are the student's monthly payments on the loans after graduation? (Round your answer to the nearest cent.)

$ _________

Answer 1

Monthly Payment $ 515.92

Explanation:

First we calculate the value of the loan after the four years:

We will calcualte that using the future value of an annuity of $12,000 for 4 years at 4%

`C * ((1+r)^(time) -1)/(rate) = FV\\`

C 12000

time 4

rate 0.04

`12000 * ((1+0.04)^(4) -1)/(0.04) = FV\\`

FV $50,957.57

Now we have to calculate the cuota of a 10 years loan with this value as the principal.

`PV / (1-(1+r)^(-time) )/(rate) = C\\`

PV $50,957.57

time 10 years x 12 months per year = 120

rate4% per year / 12 months = monthly rate = 0.00333

`50957.57 * (1-(1+0.00333)^(-120) )/(0.00333) = C\\`

C $ 515.92