Assume that you will begin saving for retirement at age 24 b

Assume that you will begin saving for retirement at age 24 by investing $3000 per year for the next 42 years. Each year you will increase your annual deposit by 5%. Therefore at age 25 you will invest 1.05times3000 = $3150 and at age 26 you will invest 1.05times3150 = $3308, etc. If your investment has an expected return of 8% determine your expected nest egg after your final payment. If an alternative and less risky investment has expected returns of 3.0% determine your expected nest egg after your final payment. What could happen that would cause you to choose one investment over the other, other than based on the calculated future value.

Solution

P = $3000, n = 42 years, r = 5% = 0.05

At age 24, Investment = $3000

At age 25, Investment = 3000*1.05 = $3150

At age 26, Investment = 3000*1.05² = $3308

Total investment in 42 years = 3000 + 3000*1.05 + 3000*1.05² + ...... + 3000*1.05⁴¹

= 3000 * ( 1 - 1.05⁴²)/(1 - 1.05)

= $ 405695.26

1. Expected return = 8%

Nest egg= 1.08*405695.26 = $438,150

2. Expected return = 3%

Nest egg = 1.03*405695.26 = $417,866