Question

Today, Bruce and Brenda each have $300,000 in an investment account. No other contributions will be made to their investment accounts. Both have the same goal: They each want their account to reach $1.5 million, at which time each will retire. Bruce has his money invested in risk-free securities with an expected annual return of 4 percent. Brenda has her money invested in a stock fund with an expected annual return of 9 percent. How many years after Brenda retires we expect Bruce to retire? Please provide the formula you used, and show your work.

Answer 1

For Bruce

Present value = $300,000

Future value = $1500,000

Here r = rate of interest = 4%

n = no of years = ?

FV = PV(1+r)^n

1500000 = 300000(1+4%)^n

5 = (1.04)^n

assume n = 41

(1.04)^41 = 5

Thus after 41 years Bruce will retire

Now For Brenda

Present value = $300,000

Future value = $1500,000

Here r = rate of interest = 9%

n = no of years = ?

FV = PV(1+r)^n

1500000 = 300000(1+9%)^n

5 = (1.09)^n

assume n = 18

(1.04)^18 = 4.7171

Now assume n = 19

1.04^19 = 5.1417

Now we can use interpolation method to find n

n	1.09^n
18	4.7171
19	5.1417
1	0.4246
?	0.2829

= 0.2829/0.4246

=0.67

Thus n = 18+0.67 = 18.67 years

Thus after 18.67 years Brenda will retire

Thus after (41-18.67) 22.33 years Brenda retires we expect Bruce to retire