Question

You have just received a windfall from an investment you made in a​ friend's business. She will be paying you $ 10,000 at the end of this​ year, $ 20,000 at the end of next​ year, and $ 30,000 at the end of the year after that​ (three years from​ today). The interest rate is 3.5 % per year.
a.What is the present value of your windfall?

b.What is the future value of your windfall in three years (on the date of the last payment)?

Answer 1

Answer:

Present Value = $55,390.58

Future value = $61,412.53

Explanation:

Given:

1st payment(C1) = $10,000

2nd payment(C2) = $20,000

3rd payment(C3) = $30,000

Interest rate(r) = 3.5% = 0.035

Present value ( PV ) = ?

Future value ( FV ) = ?

Computation of Present value:

$PV = \frac{C1}{(1+r)^1} + \frac{C2}{(1+r)^2} + \frac{C3}{(1+r)^3} \\PV = \frac{10,000}{(1+0.035)^1} + \frac{20,000}{(1+0.035)^2} + \frac{30,000}{(1+0.035)^3}\\PV = \frac{10,000}{(1.035)^1} + \frac{20,000}{(1.035)^2} + \frac{30,000}{(1.035)^3}\\PV = \frac{10,000}{1.035} + \frac{20,000}{1.071225} + \frac{30,000}{1.1087078}\\PV = 9,661.835 + 18,670.214 + 27,058.527\\PV = 55,390.5761$

Present Value = $55,390.58

Computation of Future value:

$FV = PV(1+r)^n\\= 55,390.58 (1+0.035)^3\\= 55,390.58 (1.035)^3\\= 55,390.58 (1.1087178)\\FV = 61,412.5259$

Future value = $61,412.53