You want to buy a new car that costs $48,000. Dealer A offers to lend the entire

Question

You want to buy a new car that costs $48,000. Dealer A offers to lend the entire $48,000 for a zero interest 2-year loan with monthly payments that start next month. Dealer B requires you to pay $10,000 now, followed by installments of $1,500 for the next 24 months. You observe that the market interest rate is 6%.

a) What is the net cost today of the two options? Which option offers you the cheapest financing?

b) Use a financial calculator or spreadsheet to help calculate what the interest rate would be if the financing cost from dealer A was equall to that of Dealer B.

Explanation / Answer

Answer a.

Dealer A pay 48,000 with zero interest and installment of $2,000 is paid to him each month for the two years.

Present Cost = 2000/(1 + 6/12) + 2000/(1 + 6/12)^2 + .. + 2000/(1 + 6/12)^24

= 2000/(1.005) + 2000/(1.005)^2 + .. + 2000/(1.005)^24

= $45,125.73

Dealer B require to pay $10,000 now and $1,500 per month for next 2years.

Present Cost = 10,000 + 1500/(1.005) + 1500/(1.005)^2 + .. + 1500/(1.005)^24

= $43,844.30

So, Dealer B option is cheaper than Dealer A.

Answer b.

Let i% be the the monthly rate at which Dealer A and Dealer B option are equal.

2000/(1+i) + 2000/(1+i)^2 + .. + 2000/(1+i)^24 = 10,000 + 1500/(1+i) + 1500/(1+i)^2 + .. + 1500/(1+i)^24

500/(1+i) + 500/(1+i)^2 + .. + 500/(1+i)^24 = 10,000

i = 1.5%

Annual Rate = 12 * 1.5 = 18%

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