Question

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 cash 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?

Answer 1

Ans. The formula for Present Value is

PV = P/(1+i)^n , where i is interest rate indecimals and n is number of years

Let's evaluate the installments

PVof $10000 paid one year from now using the above formula when i is 0.05 and n is 1

= $9523.8

Pv of $10000 paid two years from now, i=0.05,n=2

= $9070.3

Total present value of 3 installments= 10000+9523.8+9070.3 = $28594.1

Since the present value of installments is less than one time payment after cash discount,i.e., $28700, so he will choose the installments method of payment.

If i=3%(0.03)

Then PV of second installment = 10000/(1.03)^1 = $9708.7

PV of third installment = 10000/(1.03)^2 = $9425.96

Total pv of 3 installments = 10000+9708.7+9425.96

= $29,134.66

Since the present value of installments in this case is more than the one time cash payment of $28700, therefore he will choose to pay $28700 today.