Page 4 5. Erick borrowed $18,000 to buy a car. At alternatives-5 year loan perio
ID: 2548313 • Letter: P
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Page 4 5. Erick borrowed $18,000 to buy a car. At alternatives-5 year loan period at 6% (compounded monthly) the dealer, he was offered the following loan a) ulate the monthly payments for each of these alternatives. (5 pts) Suppose Erick had a plan of making the scheduled payments for four years and then paying the remainder of the loan off in one lump sum at the end of the 48th month. How m b) uch would he need to pay in this final payment (in addition to the originally scheduled payment for the 48h month-5 pts)?Explanation / Answer
Answer 5-a Using present value of annuity formula , we can calculate the monthly payment PV of annuity = P x {[1 - (1+r)^-n]/r} PV of annuity = present value of annuity i.e.Amount borrowed = $18000 P = Monthly payment = ? r = rate of interest per month = 6%/12 = 0.005 n = no.of months repayment = 5 years * 12 = 60 18000 = P x {[1 - (1+0.005)^-60]/0.005} 18000 = P x 51.725556 P = 347.99 Monthly Payment = $347.99 Answer 5-b Using present value of annuity formula , we can calculate the loan outstanding balance at the end of 48th month PV of annuity = P x {[1 - (1+r)^-n]/r} PV of annuity = Loan outstanding balance at the end of 48th month = ? P = Monthly payment = $347.99 r = rate of interest per month = 6%/12 = 0.005 n = no.of months repayment remaining = 12 PV of annuity = 347.99 x {[1 - (1+0.005)^-12]/0.005} PV of annuity = 347.99 x 11.61893 PV of annuity = $4043.28 Loan outstanding balance at the end of 48th month = $4043.28 Final lumsum payment towards loan = $4043.28 + $347.99 = $4391.27
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