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

Answer:

Monthly Payment $ 515.92

Step-by-step 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%

$C \times \frac{(1+r)^{time} -1}{rate} = FV$

C 12000

time 4

rate    0.04

$12000 \times \frac{(1+0.04)^{4} -1}{0.04} = FV$

FV $50,957.57

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

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV  $50,957.57

time 10 years x 12 months per year = 120

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

$50957.57 \times \frac{1-(1+0.00333)^{-120} }{0.00333} = C$

C $ 515.92