Question

Today, Bruce and Brenda each have $341,864 in an investment account. No other contributions will be made to their investment accounts. Both have the same goal; each of them wants their account to reach $1 million at the time they retire. Bruce has his money invested in risk-free securities with an expected annual return of 5%. Brenda has her money invested in a stock fund with an expected annual return of 8%. Approximately how many years after Brenda retires will Bruce retire?

Answer 1

Number of years Bruce takes to retire after Brenda's retirement is 8.05 years.

Calculations: -

Step 1: Find the number of years it will take for each $341,864 investment to grow to $1,000,000.

BRUCE: I/YR = 5; PV = -341864; PMT = 0; FV = 1000000;

and then solve for N = 21.999 years

BRENDA: I/YR = 8; PV = -341864; PMT = 0; FV = 1000000;

and then solve for N = 13.947 years

Step 2: Calculate the difference in the length of time for the accounts to reach $1 million:

Bruce will be able to retire in 22 years, or 22 – 13.95 = 8.05

8.05 years after Brenda does.