Question

A friend wants to retire in 30 years when he is 65. At age 35, he can invest $500/month that earns 5% each year. But he is thinking of waiting 15 years when he is age 50, and then investing $1,200/month to catch up, earning the same 5% per year. He feels that by investing over twice as much for half as many years (15 instead of 30 years) he will have more. A. What is the future value of each of these options at age 65, and under which scenario would he accumulate more money?

Scenario A: $__________Scenario B: $___________ , Best:___________

Answer 1

Scenario A

Investment = $ 500 x12 = $ 6000 per year

Rate of Interest = 5% per year

Total period = 30 years

So, 6000 x [ (1+5%)^30 - 1)/ 5%] = $ 398633

Scenario B

Investment = $1200 x12 = $ 14400 per year

Rate of Interest = 5% per year

Total period = 15 years

On putting values in the above formula

14400 x [ (1+5%)^15 - 1)/ 5%] = $ 310731

Since Future value of Annulity in Scenario A is $ 3.9 million and in Scenario B is $ 3.1 million, the Scenario A is accumulating more money.