The “Fly By Night” Used Car Lot uses the following to illustrate their 8.1% fina
ID: 2795247 • Letter: T
Question
The “Fly By Night” Used Car Lot uses the following to illustrate their 8.1% finance plan on a car paid over 3 years.
Cost of the car:8.1% finance charge:Total cost:Monthly payment:$10800$2624.4(that is, 8.1%/year×$10800×3 years)$13424.4$13424.436=$372.9.Cost of the car:$108008.1% finance charge:$2624.4(that is, 8.1%/year×$10800×3 years)Total cost:$13424.4Monthly payment:$13424.436=$372.9.
The first payment must be made on the date of purchase. Moreover, the dealer will pay you back 5% of the cost of the car at the end of 4 years if you return it. What is the true interest rate compounded monthly being charged?
The answer to this problem is 13.47%, please show how you would get to this answer.
Explanation / Answer
Dear Student, Lest Undestand the given problem Istallment per mont 372.9 Total number of installments = 36 istallments 1st installment you have to pay on the date of purchase it means the remaining installments was 35 installments i.e 35 months effective rate of interest = 13.47% It means rata of interest per month = 13.47/12 = 1.1225% Refund amount at the end of 4 years i.e 48th month = 1080*5% = 540 Now, lets calculate the present value of all inflows and outflows MONTH PVF @ 1.12225% AMOUNT PRESENT VALUE 0 1 372.9 372.9 1 0.9889 372.9 368.7607 2 0.977922 372.9 364.6673 3 0.967067 372.9 360.6193 4 0.956332 372.9 356.6163 5 0.945717 372.9 352.6577 6 0.935219 372.9 348.7431 7 0.924837 372.9 344.8719 8 0.914571 372.9 341.0437 9 0.904419 372.9 337.258 10 0.89438 372.9 333.5143 11 0.884452 372.9 329.8121 12 0.874634 372.9 326.1511 13 0.864925 372.9 322.5307 14 0.855324 372.9 318.9504 15 0.84583 372.9 315.41 16 0.836441 372.9 311.9088 17 0.827156 372.9 308.4465 18 0.817974 372.9 305.0226 19 0.808894 372.9 301.6367 20 0.799915 372.9 298.2884 21 0.791036 372.9 294.9773 22 0.782255 372.9 291.703 23 0.773572 372.9 288.4649 24 0.764985 372.9 285.2629 25 0.756493 372.9 282.0963 26 0.748096 372.9 278.9649 27 0.739792 372.9 275.8683 28 0.73158 372.9 272.8061 29 0.723459 372.9 269.7778 30 0.715428 372.9 266.7832 31 0.707487 372.9 263.8218 32 0.699633 372.9 260.8933 33 0.691867 372.9 257.9972 34 0.684187 372.9 255.1334 35 0.676592 372.9 252.3013 48 0.585202 540 -316.009 TOTAL 10800.65 Since the net inflow is exactly equal to cost of the car so the given effective rate is proved. Dear Student here I did the back calculations so you can understand better in this way.
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