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Homework answers / question archive / Suppose you want to buy a car, you are allowed to pay the car in a series of payments over time

Suppose you want to buy a car, you are allowed to pay the car in a series of payments over time

Economics

Suppose you want to buy a car, you are allowed to pay the car in a series of payments over time. In particular, you make three payments: $10,000 today, $10,000 1 year from today, and $10,000 2 years from today. (show your calculations when you explain) . At an interest rate of 5% per year, what is the present value of all your three payments (Hints: you need to sum up the present values of the three payments)? Suppose due to COVID, the car dealer offers you a cash discount which means that you can alternatively choose another plan where you only pay $ 28700 all at one time today. Are you going to accept the ensh discount today or insist on making the three $10,000 payments? Why? Suppose the interest rate is lowered to 3%, are you going to pay $28700 today or making the three $10,000 payments? Why? 

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1) Present Value

PV = FV * 1/(1+r)n

Therefore,

10,000/(1+ 0.05)0 + 10,000/(1+0.05)1 + 10,000/(1+0.05)2 = 10,000+ 9523.8 + 9070.2 = $28,594

2) No. I would insist on making the three $10,000 payments because, as per Present value calculations the PV of the three payments is $ 28,594, whereas after the cash discount the total amount which I will have to pay right now is $28,700 which is greater than the previous option.
Hence, I would choose to make the three $10,000 payments.

3) When the interest rate is at 3%

10,000/(1+ 0.03)0 + 10,000/(1+0.03)1 + 10,000/(1+0.03)2 = 10,000 + 9708.7 + 9425.9 = $29,143.6

If the interest rate is reduced to 3% then the present value of the three payments amounts to $29,143.6, which is greater than the amount payable if a cash discount is availed which is $28,700.
Therefore, it would be wise to opt for the cash discount rather than make the three payments in this instance.

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