
Concept explainers
To calculate: The amount that Person X can withdraw every month.
Introduction:An

Answer to Problem 32QP
Person X can withdraw $15,621.21 per month.
Explanation of Solution
Given information:
Person X is planning to maintain a balance for retirement for upcoming 30 years. Thus, Person X will invest $800 and $400 in stock and bond account respectively. The return from the stock and bond account is 10% and 6% respectively. However, Person X will combine amount of the two accounts into one account with 7% return when he retires. The period of withdrawal is assumed for 25 years.
Note:
- We must compute the
annuity payment at the time of retirement. - The savings for retirement ends and the withdrawals of retirement begins. Hence, the
present value of the retirement withdrawals will be the future value of the savings of retirement. - Thus, we must compute the future value of the stock and bond account and then we must take the sum of the two future values.
Equation to calculate the future value annuity:
Note: C denotes the annual cash flow or annuity payment, r denotes the rate of interest, and t denotes the period.
Compute the future value annuity for stock account:
Note: The investment amount and the
Hence, the future value annuity for stock account is $1,808,390.34.
Compute the future value annuity for bond account:
Note: The investment amount and the rate of return for stock account are $400 and 6% respectively. To compute the monthly return, divide the rate by 12 and multiply the number of periods by 12.
Hence, the future value annuity for stock account is $401,806.02.
Formula to calculate the overall amount saved for retirement:
Compute the overall amount saved for retirement:
Note: This total amount is the present value annuity.
Hence, the total amount that is saved for retirement is $2,210,196.36.
Formula of present value annuity to calculate the cash withdrawal per month:
Note: C denotes the annuity payment or annual cash flow, r denotes the rate of interest, and t denotes the period.
Compute the cash withdrawal per month:
Note:
- As the period of withdrawal is assumed for 25 years, t must be computed by multiplying the 25 by the number of months in a year.
- The rate of return after combining the amount of the two accounts is 7%. Hence, to compute the monthly return, divide it by 12.
Hence, the cash withdrawal per month is $15,621.21.
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