Question

An engineer is planning to buy a truck that will costs $38,000 in 5 years from now. His plan is to pay immediately half of the truck cost. The remaining will be paid based on an end-of-year payments starting with a basic payment of $2,000 yearly, and increasing yearly by the same amount B. With an interest at 6% per year, the yearly increase B is nearest to:

Answer 1

i=6%

Future cost after 5 year = 38000

Present value of the amount= 38000*(P/F, 6%,5)

= 38000*0.7472581

= 28395.81

Half of the present value = 28395.81/2 = 14197.91 paid at EOY0

Let B be the amount the yearly payment increase each year

First payment = 2000 at EOY 1 and then increase each year by B. this is a gradient series and we will use P/A and P/G factor to find present value

Present value of the payment = 14197.91 + 2000 * (P/A,6%,5) + B *(P/G,6%,5)

= 14197.91 + 2000 * 4.212363 + B * 7.934548

= 22622.63 + B* 7.934548

Present value of truck and present value of payment must be equal, therefore

28395.81 = 22622.63 + B* 7.934548

B= (28395.91-22622.63) / 7.934548

B = 727.61 = 728 (rounding off)