Question

Consider three investment plans at an annual rate of 9.38%.

Investor A: Invest $2000 per year for the first 10 years of your career. After that, make no further investments, but reinvest the amount accumulated for the next 31 years.
Investor B: Do nothing for the first 10 years. Then start investing $2000 per year for the next 31 years.
Investor C: Invest $2000 per year for the entire duration.
Note that all investments are made at the beginning of each year, the first deposit will be made today at the beginning of age 25 (n=1), and you want to calculate the balance at age of 65 (n=41).

Answer 1

Investor A = $545216 .

Investor B = $352377

Investor C = $897594

Step-by-step explanation:

Annual rate ( r ) = 9.38%

N = 41 years

Calculate the balance at age of 65

1) For Investor A

balance at the end of 10 years

= $2000 (FIA, 9.38 %, 10) (1 + 0.0938) ≈ $33845

Hence at the end of 65 years ( balance )

= $33845 (FIP, 9.38 %, 31) ≈ $545216 .

2) For investor B

at the age of 65 years ( balance )

= $2000 (FIP, 9.38%, 31) = $322159 x (1 + 0.0938) ≈ $352377

3) For Investor C

at the age of 65 years ( balance )

= $2000 (FIP, 9.38%, 41) = $820620 x (1 + 0.0938) ≈ $897594