During four years of college, Nolan MacGregor\'s student loans are $4000, $3500,

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 1.2%, compounded quarterly, while Nolan is in school and 3.7%, 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 1.2% 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 3.7%, compounded quarterly. Find the quarterly payment. (Round your answer to the nearest cent.)
$

(c) If Nolan decides to pay an additional $80 per payment, how many payments will amortize the debt? (Round your answer up to the next whole number.)
quarters

(d) How much will Nolan save by paying the extra $80 with the number of payments from part (c)? (Round your answer to the nearest cent.)
$

Explanation / Answer

Answer 1 Interest Rate 1.20% Per Quarter Loans Amounts 4000 3500 4400 5000 Loan after 1 year in 9 months 4000(1.2)^3 Amount after 1 year 4145.73491 3627.518 4560.3084 5182.16864 loan After next 3 years 4145.735*(1.012)^12 Amount after 4th year 4783.72206 4185.7568 5262.09426 5979.65257 Loan After 6 months grace @3.7% 4783.72*(1.0137)^2 Loan balance after Grace 4915.65711 4301.2 5407.22282 6144.57139 Answer 2 loan balance after grace 4915.65711 4301.2 5407.22282 6144.57139 Loan After next 10 years @3.7% Quarter      21,024.80    18,396.70      23,127.28      26,281.00 PV of loan of 10 years 20.708 20.708 20.708 20.708 Quarterly payment        1,015.30         888.39        1,116.83        1,269.12 Answer 3 Loan after 10 years      21,024.80    18,396.70      23,127.28      26,281.00 If the quarterly payment is 80 more        1,095.30         968.39        1,196.83        1,349.12 The PVF 19.1954987 18.997277 19.3238079 19.4800614 then the amount of loan in repaid in 34 quarter 33 quarters 34.5 quarters 35 quarters Answer 4 Quarterly Payments 1095.298 968.386 1196.828 1349.123 No. of quarters 34 33 34.5 35 Total Payment 37240.1408 31956.737 41290.569 47219.2989 Loan amount 4915.657 4301.200 5407.223 6144.571 Interest Amount 32324.484 27655.537 35883.346 41074.727 as per no addition of $80 Quarterly Payments 1015.29826 888.38598 1116.82809 1269.12282 No. of payments 40 40 40 40 Total Payment 40611.9304 35535.439 44673.1234 50764.913 Loan Amount 4915.657 4301.200 5407.223 6144.571 Interest Amount 35696.273 31234.239 39265.901 44620.342 Therefore saving by paying extra As per old payment interest is 35696.273 31234.239 39265.901 44620.342 As per new payment interest is 32324.4837 27655.537 35883.3461 41074.7275 Savings 3371.790 3578.702 3382.554 3545.614

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