This problem is a complex financial problem that requires several skills, perhaps some from previous sections. During four years of college, Nolan MacGregor's student loans are $4,000, $3,500, $4,400, and $5,000 for freshman year through senior year, respectively. Each loan amount gathers interest of 1%, 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 (in dollars) after the grace period? Assume the freshman year loan earns 1% 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 (in dollars). (Round your answer to the nearest cent.) $ (c) If Nolan decides to pay an additional $60 per payment, how many payments will amortize the debt? (Round your answer to two decimal places.) payments What amount (in dollars) should be added to the last payment to pay the loan in full? (Round your answer to the nearest cent.) $ (d) How much will Nolan save (in dollars) by paying the extra $60 with each payment? (Round your answer to the nearest cent.) $
This problem is a complex financial problem that requires several skills, perhaps some from previous sections. During four years of college, Nolan MacGregor's student loans are $4,000, $3,500, $4,400, and $5,000 for freshman year through senior year, respectively. Each loan amount gathers interest of 1%, 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 (in dollars) after the grace period? Assume the freshman year loan earns 1% 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 (in dollars). (Round your answer to the nearest cent.) $ (c) If Nolan decides to pay an additional $60 per payment, how many payments will amortize the debt? (Round your answer to two decimal places.) payments What amount (in dollars) should be added to the last payment to pay the loan in full? (Round your answer to the nearest cent.) $ (d) How much will Nolan save (in dollars) by paying the extra $60 with each payment? (Round your answer to the nearest cent.) $
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:This problem is a complex financial problem that requires several skills, perhaps some from previous sections.
During four years of college, Nolan MacGregor's student loans are $4,000, $3,500, $4,400, and $5,000 for freshman year through senior year, respectively. Each loan amount gathers interest of 1%, 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 (in dollars) after the grace period? Assume the freshman year loan earns 1% 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 (in dollars). (Round your answer to the nearest cent.)
$
(c) If Nolan decides to pay an additional $60 per payment, how many payments will amortize the debt? (Round your answer to two decimal places.)
payments
What amount (in dollars) should be added to the last payment to pay the loan in full? (Round your answer to the nearest cent.)
$
(d) How much will Nolan save (in dollars) by paying the extra $60 with each payment? (Round your answer to the nearest cent.)
$
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