Question

Assuming year-end cash flows: a. The Chicago Hope Hospital purchased a MRI machine for 2 million dollars, using 5 year loan at 10% interest. What will be the annual payment for the machine? b. The Price of the MRI machine (2mil) is rising at a fixed rate of 5% each year. How much would it cost to replace the MRI machine five years from now?

Answer 1

Computation of Annual Payment for the machine :-

This can be solved using the present value of future annuities = P*(1-(1+r)^-n)/r

Present value of future annuities is given as $ 2 Million or $ 2,000,000/-

P is Annual Payment = ?

r is Rate of interest per annum = 10%

n is no of years = 5

2000000=P*(1-(1+0.10)^-5)/0.10

P is = 2000000/3.790786

P is $ 527,595/-

So Annual Payment is $ 527,595/-.

b) Price of the machine after 5 years is caluclated using the Future value formula as below :-

Future value = Present value*(1+r)^n

Present value is $ 2,000,000/-

r is rate of interest = 5%

n is no of years = 5

Future value after 5 years is = (2000000*(1+0.05)^5) = (2000000*1.2762815625)

Future value is = $ 2,552,563.13/-

Cost to replace MRI machine after five years will be $2,552,563.13/-