A friend wants to work for 2 years then return to school full time for a master’
ID: 2653695 • Letter: A
Question
A friend wants to work for 2 years then return to school full time for a master’s degree. OPTION A: He can invest $1,000/month in a mutual fund that earns 6% annually, for 2 years. But he is thinking of waiting five years, and investing only $500/month for the whole five years (he wants to enjoy life - OPTION B), earning the same 6% per year. He feels that by investing twice as much for 2 years instead of 5 years he might have less to live on for the two years of full time school, but will finish his degree three years earlier.
A. How much will he have saved under Option A?
B. How much will he have saved under Option B?
C. When he starts his masters, under Option A, how much can he withdraw per month, for 2 years (assume he continues to earn 6%)?
D. How much can he withdraw per month, for 2 years, under Option B, (assume he continues to earn 6%)?
E. Which option would you choose, and why?
Explanation / Answer
(A)
Option A: 6% annual rate = 0.5% per month
Present value of $1,000 invested per month at 0.5% rate for 24 months
= $1,000 x (Present Value Interest factor of Annuity, 0.5%, 24 periods)
= $1,000 x 22.5629 (From PVIFA table)
= $22,562.90
Option B: 6% annual rate = 0.5% per month
Present value of $500 invested per month at 0.5% rate for 60 months
= $500 x (Present Value Interest factor of Annuity, 0.5%, 60 periods)
= $500 x 51.7256 (From PVIFA table)
= $25,862.80
(C) When he starts his masters, he will have an amount in hand worth [$1,000 x Future Value Interest factor of Annuity, 0.5%, 24 periods)] = $1,000 x 25.432 (From FVIFA table)
= $25,432
If he wants to withdraw $A per month for 24 months at 0.5% then
$25,432 = $A x Present Value Interest factor of Annuity, 0.5%, 24 periods
= $A x 22.5629 (From PVIFA table)
Or, A = 25,432 / 22.5629 = $1,127.16
(D) When he starts his masters, he will have an amount in hand worth [$500 x Future Value Interest factor of Annuity, 0.5%, 24 periods)] = $500 x 25.432 (From FVIFA table)
= $12,716
If he wants to withdraw $A per month for 24 months at 0.5% then
$12,716 = $A x Present Value Interest factor of Annuity, 0.5%, 24 periods
= $A x 22.5629 (From PVIFA table)
Or, A = 12,716 / 22.5629 = $563.58
(E) I would have chosen Option (A) because during my college I will be able to withdraw about twice amount of money compared to that under option (B).