Question

12. Bob, age 35, has already accumulated $100,000 in retirement assets. He expects to retire at age 65 and live until age 90. He expects to earn 8% before retirement and 6% after retirement. If he makes no additional contributions to his account and he receives a fixed (non-increasing) monthly annuity from the account for life, what is the amount he could withdraw at the beginning of each month in retirement? a. $3,682.12 b. $6,451.13 c. $7,715.08 d. $8,212.04 Annuity in the m ot annronrinta tune of yesting schedule for a

Can I get assistance with this question.

Answer 1

Currently he has $100,000 and expects to retire at 65 and current age is 35. That means we have to find out future value (FV) of $100,000 after 30 years compounded at 8% interest.

We have the formula:

Where, A = Present value of the amount

n = number of periods

i = rate of interest

Therefore,

That means by the age of 65 his retirement assets will become $1,006,265.69

He retires at 65 and expects to live till 90, the time period is 25 years

The question says that he wants to withdraw at the beginning of each month a fixed amount. To find that amount we have to use the formula of Present Value of Future Annuity due (PVFA);

Formula:

$PVFA = P \left \{ \left [ \frac{(1+i/a)^{na}-1}{i/a(1+i)^{na}} \right ](1+i/a) \right \}$

Where,

P = Annuity

i = rate of interest

n = number of periods

a = number of withdrawals in a year

na = total number of withdrawals

So let us put the values in the formula:

$1,006,265.69= P \left \{ \left [ \frac{(1+0.06/12)^{25*12}-1}{0.06/12(1+0.06/12)^{25*12}} \right ](1+0.06/12) \right \}$

$1,006,265.69= P \left \{ \left [ \frac{3.4649698}{0.0223249} \right ](1.005) \right \}$

$P = \frac{1,006,265.69}{155.982898}$

$=6451.13$

Therefore, He will get to withdraw $6,451.13 at the beginning of every month.

Note: In my calculations I have not rounded off intermediate calculations.