Problem 55 John wants to program for a fouryear finance plan

Problem 5-5 John wants to program for a four-year finance plan. He plans to spend $25,000 to buy a car in two years later; spend $2,500 to buy furniture in three years later; and to spend $250,000 to buy a house in the fourth year. How much money John should deposit to the bank at 15% interest compounded annually? Students shall draw simple Cash Flow Diagram, and use Pv Equivalency Method to solve this problem. | PV Fv Solve for Answer #\'s of years Interest i PMT 15% 15% 15% 15% 0 0 0 0 $25,000 Pv1 -$2,500 $250,000 Pv3 2 Pv2 4 John should deposit the money to bank at beginning of year 1 Pv (total)

Solution

FVF(15%,2 yrs) = (1.15)² = 1.3225

FVF(15%,3 yrs) = (1.15)³ = 1.5209

FVF(15%,4 yrs) = (1.15)⁴ = 1.7490

A) Present value of buying a car in two years (Pv1) = Future Value/FVF(15%,2 yrs)

= $25,000/1.3225 = $18,903.60

B) Present value of buying furniture in three years (Pv2) = Future Value/FVF(15%,3 yrs)

= $2,500/1.5209 = $1,643.76

C) Present value of buying a house in fourth year (Pv3) = Future Value/FVF(15%,4 yrs)

= $250,000/1.7490 = $142,938.82

Total Present Value = $18,903.60+$1,643.76+$142,938.82

= $163,486.18 (or $163,486 rounded off)

Therefore, John should deposit the money to bank at beginning of year 1 of $163,486.