You are planning to save for retirement over the next 30 years. To do this, you will invest $850 per month in a stock account and $350 a month in a bond account. The return of the stock account is expected to be 10 percent, and the bond account will pay 6 percent. When you retire, you will combine your money into an account with an 5 percent return. how much can you withdraw each month from your account assuming a 25-year withdrawal period?

An amount of $13,287.70 can be withdrawn each month from your account assuming a 25-year withdrawal period.

Explanation:

To calculate the total amount saved for 30 years after retirement, we us the formula for calculating the future value of ordinary annuity for both stock and bond as follows:

Future Value of Stock

FVs = M × {[(1 + r)^n - 1] ÷ r} (1)

Where,

FVs = Future value of the amount invested in stock after 30 years =?

M = Monthly investment = $850

r = Monthly interest rate = 10% ÷ 12 = 0.8333%, 0.008333

n = number of months = 30 years × 12 months = 360

Substituting the values into equation (1), we have:

FVs = $850 × {[(1 + 0.008333)^360 - 1] ÷ 0.008333} = $1,921,414.74

Future Value of Bond

FVb = M × {[(1 + r)^n - 1] ÷ r} (2)

Where,

FVb = Future value of the amount invested in bond after 30 years =?

M = Monthly investment = $350

r = Monthly interest rate = 6% ÷ 12 = 0.50%, 0.0050

n = number of months = 30 years × 12 months = 360

Substituting the values into equation (2), we have:

FVb = $350 × {[(1 + 0.0050)^360 - 1] ÷ 0.0050} = $351,580.26

Amount that can be withdrawn monthly for 25-year withdrawal period

To calculate this, we use the formula for calculating the present value of an ordinary annuity as follows:

PV = P × [{1 - [1 ÷ (1+r)]^n} ÷ r] …………………………………. (3)

Where;

PV = Combined present values of stock and bond investments after retirement = FVs + FVb = $1,921,414.74 + $351,580.26 = $2,272,995.00

P = Monthly withdrawal = ?

r = Monthly interest rate = 5% ÷ 12 = 0.4167%, or 0.004167

n = number of months = 25 years * 12 months = 300

Substitute the values into equation (3) to have:

$2,272,995.00 = P × [{1 - [1 ÷ (1 + 0.0047)]^300} ÷ 0.0047]

$2,272,995.00 = P × 171.060047040905

P = $2,272,995.00 / 171.060047040905

P = $13,287.70

Therefore, $13,287.70 can be withdrawn each month from your account assuming a 25-year withdrawal period.

d. all of the above are true.

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