Question

Your uncle has $300,000 today. Assume he can earn 9.18% on his investments. He now wants to retire in 10 years. Here is his situation:

a. He wants to withdraw $35,000 every two years, beginning 12 years from today for 10 equal, every two-year (i.e. every other year) withdrawals.

b. He has to pay for his daughter’s college beginning in 5 years at $20,000 for four years (i.e. he has to make a payment in year 5, 6, 7, and 8).

c. He just inherited some money, totaling $40,000, which he will receive 8 years from today.

He also wants to leave you whatever he can afford 20 years from today and still meet all his other goals. How much is the amount of money you will receive?

Answer 1

Value of today's investments = $300,000

Annual interest rate = 9.18%

2 year interest rate = (1+Annual interest rate)² -1 = (1+9.18%)² -1 = 19.2027%

Years to retirement = 10 years

a.

He needs to withdraw $35,000 every 2 years for 10 equal withdrawals

The retirement amount he needs at retirement can be calculated using the PV for an ordinary annuity formula

Where C is the withdrawal = $35,000

i = 2 year interest rate = 19.2027%

n = number of 2 year periods = 10

PV = $150,799.67

Your uncle needs $150,799.67 at retirement

Retirement fund = $150,799.67

b.

He has to pay for his daughter’s college beginning in 5 years at $20,000 for four years

Present value of these payments at year 5 can be calculated using the PV for an annuity-due formula

Where C is yearly payment = $20,000

i = annual interest rate = 9.18%

n = number of periods = 4

PV = $70,463.93

Your uncle needs $70,463.93 at the end of 5 years for his daughter's college

1.

Value of his initial investments after 5 years = Value of today's investments *(1+9.18%)⁵

= $300,000 *(1+9.18%)⁵ = $465,411.07

2.

Value of the above investment after accounting for daughter's college = Value of his initial investments after 5 years - Present value of amount needed for daughter's college

= $465,411.07 - $70,463.93 = $394,947.14

3.

Value of the investments in 2 after another 3 years (at year 8) = $394,947.14 *(1+9.18%)³ = $514,006.06

4.

Value of the above investment after accounting for inheritance = Value of investments at year 8 + inheritance

= $514,006.06 + $40,000 = $554,006.06

5.

Value of the investments in 5 after 2 years at his retirement (at year 10) = $554,006.06 *(1+9.18%)² = $660,390.32

6.

Value of the above investment after accounting for retirement = Value of investments at retirement - retirement fund

= $660,390.32 - $150,799.67 = $509,590.65

7.

Value of the above investment after another 10 years (at year 20) = $509,590.65*(1+9.18%)¹⁰ = $1,226,457.06

This is the amount that you will receive

You will receive $1,226,457.06 after 20 years