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

Accepted Solution

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%[tex]C \times \frac{(1+r)^{time} -1}{rate} = FV\\[/tex] C 12000time 4rate    0.04[tex]12000 \times \frac{(1+0.04)^{4} -1}{0.04} = FV\\[/tex] FV $50,957.57 Now we have to calculate the cuota of a 10 years loan with this value as the principal.[tex]PV \div \frac{1-(1+r)^{-time} }{rate} = C\\[/tex] PV  $50,957.57 time 10 years x 12 months per year = 120rate4% per year / 12 months = monthly rate =  0.00333[tex]50957.57 \times \frac{1-(1+0.00333)^{-120} }{0.00333} = C\\[/tex] C $ 515.92