Please show all of the steps!! Thank you! :) During four years of college, Nolan
ID: 2801968 • Letter: P
Question
Please show all of the steps!! Thank you! :)
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 1.4%, 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 1.4% 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.)
$
(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.)
(c) If Nolan decides to pay an additional $50 per payment, how many payments will amortize the debt? (Round your answer up to the next whole number.)
(d) How much will Nolan save by paying the extra $50 with the number of payments from part (c)? (Round your answer to the nearest cent.)
Explanation / Answer
FV = P *(1+R)^N Ist year Iind Year IIIrd Year Ivth Year Total Loan after graduation Grace period P 4,000.00 3500 4400 5000 17,414 R 0.35% 0.35% 0.35% 0.35% 0.75% N 15 11 7 3 2 =4000*(1+.35%)^15) Loan Balance 4,215 3,637 4,509 5,053 17414 17,676 After Grace Period Principal 17,676 Interest 3.0% 0.7500% N period 10 40 Instalmment $ 513 Quaterly Payment= =(17676*.75%*(1+.75%)^40)/((1+.75%)^40-1) $ 513 If nolan decide to pay additional $50 563=(17676*.75%*(1+.75%)^N)/((1+.75%)^N-1) By solving this N=36 Money Nolan will save Instalment saved 4*563 2,252 Less: Payment Made =50*36 1,800 Net Money Save 452
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