Question

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 2%, 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 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.) $ 17905.42 (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.) $ 519.80 (c) If Nolan decides to pay an additional $90 per payment, how many payments will amortize the debt? (Round your answer to two decimal places.) 33.29 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.) $ 241 x (d) How much will Nolan save (in dollars) by paying the extra $90 with each payment? (Round your answer to the nearest cent.) $ 491.76

Answer 1

176.08 should be added to last payment i.e. 33rd installment to pay the loan in full.

int Opening Bal Installme Interest Principal Closing Loa ance (openin installmen Balance (previous cl (519.8+9 g balancnt - intere (opening-p Installment osing) 0 e x 0.75%) st) rincipal) 1 17905.42 609.8 134.29 475.51 17429.91 2 17429.91 609.8 130.72 479.08 16950.83 3 16950.83 609.8 127.13 482.67 16468.17 4 16468.17 609.8 123.51 486.29 15981.88 5 15981.88 609.8 119.86 489.94 15491.94 6 15491.94 609.8 116.19 493.61 14998.33 7 14998.33 609.8 112.49 497.31 14501.02 8 14501.02 609.8 108.76 501.04 13999.98 9 13999.98609.8 105 504.8 13495.18 1013495.18 609.8 101.21 508.59 12986.59 11 12986.59 609.8 97.399 512.4 12474.19 12 12474.19 609.8 93.556 516.24 11957.95 13 11957.95 609. 8 89.685 520.12 11437.83 14 11437.83 609.8 85.784 524.02 10913.81 15 10913.81 609. 8 81.854 527.95 10385.87 16 10385.87 609.8 77.894 531.91 9853.962 17 9853.962 609.8 73.905 535.9 9318.066 9318.066609. 8 69.885 539.91 8778.152 19 8778.152 609. 8 65.836 543.96 8234.188 8234.188 609.8 61.756 548.04 7686.144 21 7686.144 609.8 57.646 552.15 7133.991 22 7133.991 609.8 53.505 556.3 6577.695 23 6577.695 609.8 49.333 560.47 6017.228 24 6017.228 609.8 45.129 564.67 5452.557 25 5452.557 609. 8 40.894 568.91 4883.652 26 4883.652 609.8 36.627 573.17 4310.479 27 4310.479 609. 8 32.329 577.47 3733.008 28 3733.008 609.8 27.998 581.8 3151.205 29 3151.205 609.8 23.634 586.17 2565.039 30 2565.039 609.8 19.238 590.56 1974.477 31 1974.477 609.8 14.809 594.99 1379.485 32 1379.485 609.8 10.346 599.45 780.0316 33 780.0316 609.8 5.8502 603.95 176.0819 18