A 30-year old professional invests $575 per month into a fund which earns 9% int

Question

A 30-year old professional invests $575 per month into a fund which earns 9% interest compounded monthly.

a) If the professional invests this amount each month until age 60, what will be the balance of the fund?

b) If the professional makes no further deposits and no withdrawals after age 60, but lets the fund continue to generate interest, what will be the balance of the fund when the professional retires at age 65?

c) If the professional then withdraws equal monthly amounts from the fund from age 65 to 85, how much does the professional withdraw each month?

Explanation / Answer

Answer a.

Monthly deposit = $575
Annual Interest Rate = 9%
Monthly Interest Rate = 9%/12 = 0.75%
Number of monthly deposits = 30*12 = 360

Accumulated Sum = $575 * FVIFA (0.75%, 360)
Accumulated Sum = $575 * (1.0075^360 - 1) / 0.0075
Accumulated Sum = $1,052,677.50

So, balance of fund at age 60 is $1,052,677.50

Answer b.

Balance of fund at age 60 = $1,052,677.50
Monthly Interest Rate = 0.75%

Value of Fund at age 65 = $1,052,677.50 * 1.0075^60
Value of Fund at age 65 = $1,648,157.19

Answer c.

Value of Fund at age 65 = $1,648,157.19
Monthly Interest Rate = 0.75%

Monthly Withdrawal = $1,648,157.19 / PVIFA (0.75%, 240)
Monthly Withdrawal = $1,648,157.19 / [(1 - (1 / 1.0075)^240) / 0.0075]
Monthly Withdrawal = $1,648,157.19 / 111.14495
Monthly Withdrawal = $14,828.90

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