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, and variables used.

a) 20.01

b) 18.42

c) 22.36

d) 16.1

Answer 1

We can use the following formula:

F= P*(1+r)^t; where F= Future value, P is Present value, r is expected annual return and t is number of years.

For Brenda,

given that expected annual return is 9%. So, Using the formula, 1500000= 300000*(1+9%)^t

5= 1.09^t

t= 18.68

Brenda takes 18.68 years to retire.

For Bruce,

given that expected annual return is 4%. So, Using the formula, 1500000= 300000*(1+4%)^t

5= 1.04^t

t= 41.04

Bruce takes 41.04 Years to retire.

So, Bruce retires after 41.04-18.68= 22.36 Years after Brenda retires. (Option c)