Question

Alan has just started work and he has been wanting to buy a sleek power boat for some time. Rather than purchase and finance now, he plans to save money to buy it. He plans to deposit a fixed amount every month into a bank account that pays 3% a year, compounded monthly. His first deposit will be made a month from now. How much must each deposit be, if he is going to buy the boat in 5 years and the boat will cost $50,000 then?

b.) You are considering the purchase of an apartment complex that will generate net cash flows each of the next 20 years, starting at $400,000 in Year 1. You normally demand a 10% rate of return on such investments. Future cash flows after year 1 are expected to grow with inflation at 4% per year. How much would you be willing to pay for the complex today if it will have to be torn down in 20 years, and the land could be sold for a net amount of $5 million in year 20?

Answer 1

1: Using financial calculator
Input: I/Y = 3/12

N = 60

FV = 50000

Solve for PMT as -773.43

Hence the monthly deposit = $773.43

2: Present value today = PV of annuity with growth + PV of future value

= (P/ (r-g)) * (1- ((1+g)/(1+r))^n) + FV/(1+r)^n

= (400000/(10%-4%))* (1-(1.04/1.1)^20) + 5000000/1.1^20

= 4495356.71 + 743218.14

= 5238574.85