Answer:
An amount of $13,287.70 can be withdrawn each month from your account assuming a 25-year withdrawal period.
Step-by-step 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Amount that can be withdrawn monthly for 25-year withdrawal period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Therefore, $13,287.70 can be withdrawn each month from your account assuming a 25-year withdrawal period.