Question

Derek has the opportunity to buy a money machine today. The money machine will pay Derek $44,309.00 exactly 16.00 years from today. Assuming that Derek believes the appropriate discount rate is 9.00%, how much is he willing to pay for this money machine?

Answer 1

$11,160.097

Step-by-step explanation:

Data provided in the question:

Future value of machine = $44,309.00

Time, n = 16 years

Discount rate, r = 9.00% = 0.09

Now,

The amount Derek is will to pay will be the present value of the machine

Also,

we know

Future value = Present value × (1 + r)ⁿ

on substituting the respective values, we get

$44,309.00 = Present value × (1 + 0.09 )¹⁶

or

$44,309.00 = Present value × 3.97

or

Present value = $44,309.00 ÷ 3.97

or

Present value = $11,160.097