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. Toreward your achievement, you decide to buy your dream car which costs $80, 000. Thecar dealer requires an immediate deposit of $10,000 and offers you the following twofinancing options for the rest of the car cost:
Option A: Pay nothing for the first two years and then $1000 monthly repayments atrate 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

As we have paid $10000 at the begining of this contract,

We have to pay back $70000 with the options mentioned above.

lets say a year has 360 days for computational purpose. now for daily interest rate we have (12/360)% = (0.0333%) daily interest hence monthly interest will be 1.000333^30 =1.010047%

We equating present value of all installments to the cost paid today.

70000 = 1000(1/1.010047+(1/1.010047)^2+....+(1/1.010047)^n)=NPER(1.01047%,-1000,70000,0,1) =119.5 months required to repay and we have paid nothing in first 2 years therfore it will take 144 months to repay optionA

12% paid continuously = (1+12%/360)^360 =1.127474% per annum

and months to repay the loan is nper(12.7474%/12,-1000,70000,0,1) = 125 months

hence option be has less pay back period thats why lower debt and finaciial cost

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