You have just finished your degree and landed a well paid job in a consulting fi

Question

You have just finished your degree and landed a well paid job in a consulting firm. To reward your achievement, you decide to buy your dream car which costs $80,000. The car dealer requires an immediate deposit of $10, 000 and offers you the following two financing options for the rest of the car cost: Option A: Pay nothing for the first two years and then 81000 monthly repayments at rate 12% per annum compounded daily. Option B: Start monthly repayments of 1000 immediately at 12% per annum rate com- pounded continuously. (a) How many years will it take to repay the loan for each of the proposed options? [3.5 marks] (b) Which option will you take if your goal is to lower the debt total financial cost? [1 marks]

Explanation / Answer

for option 1

when you are going to pay after 2 years and pay thereafter 2 years $1000 monthly with 12 % compounded daily we need to find effetive monthly interest and that should be (1.00033)^360 = 1.12747474% i.e. 12.747% if compounded daily.

months to repay back required can be found using NPER formula available in excel

NPER = (12.747%/12,-1000,70000,0,1) = 119.5 months + 24 months of non payment

Similarly for option 2

Effective period will be (1+(12%/12)^12 = 1.1268 that is 12.68% monthly compounded return

NPER = (12.68%/12,-1000.70000,0,1) = 125 months

hence option B would be the better option as repayment period is less as well as effective interest is lower than that of daily compounding 12.68% < 12.747%

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