You decide to purchase a car which sells for $27,000. You agree to pay $2,500 no

Question

You decide to purchase a car which sells for $27,000. You agree to pay $2,500 now and desire to pay the remainder with 48 equal monthly payments. You are asked to sign a contract where your monthly payment will be $805 per month for 48 months for a total of 48 payments. They disclose that you will be paying back a grand total of $38,640 which excludes your down payment of $2,500, $24,500 for the original amount that you financed plus $14.140 in interest charges. What is the effective interest rate are you being charged on this car loan? After making 18 payments, you decide to payoff the loan. What amount should you include with your final payment at the end of the 18th month to completely pay off this loan? State the assumptions that you use to arrive at your final payment amount and show all your calculations.

Explanation / Answer

(a) Here the case is : Purchase of car with a Price of $27000 with a downpayment of $2500 & 48 Monthly Inst of $805. So the Principal of this contract is $27000-$2500 = $24500 Finance Charge ie Total Int paid is =(2500+48*$805) - $27000 = 14140 Effective rate on installment loan = 2 X Annual No of payments X Interest/[(Total no. of payments + 1) X Principal] Effective rate for installment loan (EIR) =(2 X 12 X $14140)/[(48+1) X $24500] = 28.27% (b) Interest rate on Loan is found by using Excel 'Rate' function. Int Rate = rate(nper,PMT,PV) where nper is no of instalment, PMT is loan inst & PV is Loan amount As ours is monthly inst, we will get monthly rate. So we need to multiply it by 12 to get annual Int rate. So Annual Int rate i =12*RATE(48,-805,24500) = 24.46% Now we use Future value FV function of exel to find the principal outstanding at end of 18 months. Prinicpal at end of 18Month = FV(Rate,nper,PMT) = FV(24.46%/12,18,-805) = $17296 So at end of 18 months, you can make a final payent of $17296 to cloe the Loan

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