Question

Student Loan Program

The National Direct Student Loan (NDSL) program allows college students to borrow funds from the federal government. The contract stipulates that the annual percentage rate of interest is 0 percent until 12 months after the student ceases his or her formal education (defined as as least half-time enrollment). At that time, interest becomes 4 percent per year. The maximum repayment college period is 10 years. Assume that the student borrows $10,000 in the beginning of the first year of college and completes his or her education in four years. Loan repayments begin one year after graduation.

Required:

A. Assuming that the student elects the maximum payment period, what are the uniform annual loan repayments? (Assume all repayments occur at the end of the year)

B. If the rate of interest on savings deposits is 6 percent, what is the minimum amount the student has to have in a bank account one year after graduation to make the loan payments calculated in part (a)?

C. Are recipients of the NDSL program receiving a subsidy? If so, what is the present value of the subsidy when the loan is taken out?

Answer 1

Answer:-

A). Assuming that the student elects the maximum payment period, what are the uniform annual loan repayments?

Annuity factor = (1 - ( 1 + r) ^-10) / r ( r = 4% = 0.04 , t = 10 years)

= ( 1 - ( 1 + 0.04 )^-10) / 0.04

= 8.1108

Annuity factor = 8.1108

PV	payment * annuity factor
$10,000	Payment * 8.1108
= 10,000 / 8.1108 = $1233.04	Payment

(B). If the rate of interest on savings deposits is 6 percent, what is the minimum amount the student has to have in a bank account one year after graduation to make the loan payments calculated in part (a)?

Annuity factor = (1 - ( 1 + r) ^-10) / r ( r = 6% = 0.06 , t= 10 years)

= ( 1 - ( 1 + 0.06 )^-10) / 0.06

=7.3600

Annuity factor = 7.3600

PV	Payment * Annuity factor
	$ 1,233 * 7.3600 = $9,074.98

C. Are recipients of the NDSL program receiving a subsidy? If so, what is the present value of the subsidy when the loan is taken out?

ans;- Indeed, the NDSL beneficiaries are getting an endowment .Recall that five years have gone since the understudy got the $10,000 credit .The present estimation of the yearly advance repayments.($1,233)amounts .