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 $250 per month in a bond account. The return of the stock account is expected to be 11 percent, and the bond account will return 6 percent. When you retire, you will combine your money into an account with a return of 5 percent. How much can you withdraw each month from your account assuming a 25-year withdrawal period

The withdrawal period is the minimum amount of time between the administration of the final dose of medication and the manufacture of meat or other food items produced from animals.

What is a withdrawal period and why is it important?

Withdrawal times take into account how long it takes an animal to digest a substance that has been given to it as well as how long it takes for the substance's concentration in its tissues to drop to a safe, acceptable level.

According to the question:

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Amount that can be withdrawn monthly for 25-year withdrawal period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

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