Question

Mr. Chan's retirement plan includes an equal semiannual withdrawal from a bank account for 20 years starting from the time of his retirement. The account balance is $80,000 at the beginning of the retirement period, and the interest rate is 8% per year compounded semiannually. At the time of retirement, he plans on using up the money completely in 20 years. (Round all your answers to two decimal places.)

a. How much can Mr. Chan withdraw from the bank account semiannually if each equal withdrawal is made at the end of every half year after retirement?
b. How much can Mr. Chan withdraw from the bank account semiannually if each equal withdrawal is made at the beginning of every half year after retirement?

Answer 1

The student's questions relate to determining annuity payments for Mr. Chan's retirement plan. These payments depend on whether they are made at the end or beginning of each semiannual period, which requires adjustment of the annuity formula accordingly.

Step-by-step explanation:

The questions the student has asked pertain to annuity calculations with compounded interest, which are common in retirement planning scenarios.

a. To determine how much Mr. Chan can withdraw semiannually at the end of every half year, we can use the formula for the annuity (ordinary annuity) where payments are made at the end of each period. The formula to use is PMT = P × (r/n) / [1 - (1 + r/n)^(-nt)], where PMT is the annuity payment, P is the principal amount, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time in years. Substituting the provided values, we calculate Mr. Chan's withdrawal amount.

b. If Mr. Chan makes each equal withdrawal at the beginning of every half year, this becomes an annuity due. In this case, the formula to calculate the annuity payment is modified slightly to account for the immediate first withdrawal and the present value of this type of annuity being higher. The payment is calculated similarly but multiplied by (1 + r/n) to shift the payment to the beginning of the period.