Question

During four years of college, Nolan MacGregor's student loans are $4000, $3500, $4400, and $5000 for freshman year through senior year, respectively. Each loan amount gathers interest of 1.9%, compounded quarterly, while Nolan is in school and 3%, compounded quarterly, during a 6-month grace period after graduation.

(a) What is the loan balance after the grace period? Assume the freshman year loan earns 1.9% interest for 3/4 year during the first year, then for 3 full years until graduation. Make similar assumptions for the loans for the other years. (Round your answer to the nearest cent.) the answer is not 17652.96 or 17.67 or 21828.40/ 17951.9

(b) After the grace period, the loan is amortized over the next 10 years at 3%, compounded quarterly. Find the quarterly payment. (Round your answer to the nearest cent.) $ the answer is not 21421.39 or 1,054 or 442.12 or 521.15

(c) If Nolan decides to pay an additional $70 per payment, how many payments will amortize the debt? (Round your answer up to the next whole number.) the RIGHT answer is 35 quarters!! not 33

(d) How much will Nolan save by paying the extra $70 with the number of payments from part (c)? (Round your answer to the nearest cent.) $ the answer is not 784.84 or 1124 or 5270 or 124.84. or 746.9

Answer 1

(a)

(b) Outstanding Loan Balance = $ 17867.26, Loan Tenure = 10 years or 40 quarters, Interest Rate = 3% per annum or 0.75% per quarter.

Let the quarterly payments be $ K

Therefore, 17867.26 = K x (1/0.0075) x [1-{1/(1.0075)^(40)}]

K = $ 518.69 per quarter

(c) If Nolan pays $ 70 over and above the regular quarterly payment, the new quarterly payment = K' = 70 + 518.69 = $ 588.69, Loan Balance = $ 17867.26 and Interest Rate = 3% per annum or 0.75% per quarter

Let the loan tenure be n quarters

Therefore, 17867.26 = 588.69 x (1/0.0075) x [1-{1/(1.0075)^(n)}]

n = 34.6 or 35 quarters approximately.

(d) First Repayment Option:

Quarterly Repayments = $ 518.69 and Tenure = 40 Quarters

Interest Paid = IP1 = Total Amount Paid - Principal Borrowed (TLB) = 518.69 x 40 - 17867.26 = $ 2880.34

Second Repaymente Option:

Quarterly Repayments = $ 588.69 and Tenure = 35 Quarters

Interest Paid = IP2 = Total Amount Paid - Principal Borrowed (TLB) = 588.69 x 35 - 17867.26 = $ 2736.89

Savings = IP1 - IP2 = 2880.34 - 2736.89 = $ 143.45