Your auntie is planning to retire in 6 years. Currently, she has $55,000 in a bond account and $82,000 in a stock account. She plans to add $9,000 per year at the end of each of the next 3 years to her bond account. The stock account will earn a return of 8% per year and the bond account will earn a return of 4% per year. On retirement, your auntie will transfer her money to a savings account which earns an interest of 2% per year. She hopes to withdraw an equal amount for each of the next 15 years at the end of each year and have nothing left. Discuss how you will determine the amount your auntie is able to withdraw each year during her retirement, and solve for it. (23 marks)
Question
Your auntie is planning to retire in 6 years. Currently, she has 82,000 in a stock account. She plans to add $9,000 per year at the end of
each of the next 3 years to her bond account. The stock account will earn a return of
8% per year and the bond account will earn a return of 4% per year.
On retirement, your auntie will transfer her money to a savings account which earns an
interest of 2% per year. She hopes to withdraw an equal amount for each of the next 15
years at the end of each year and have nothing left.
Discuss how you will determine the amount your auntie is able to withdraw each year
during her retirement, and solve for it.
(23 marks)
Solution
To determine the amount your auntie is able to withdraw each year during her retirement, we need to calculate the future value of her bond and stock accounts at the time of her retirement, and then calculate the annuity payment she can withdraw from this total amount each year during her retirement.
Step 1: Calculate the future value of the bond account First, we need to calculate the future value of the bond account after 3 years when she stops adding $9,000 per year. The formula for the future value of a series of payments (annuity) is:
FV = P * [(1 + r)^n - 1] / r
where: P = $9,000 (annual payment) r = 4% (annual interest rate) n = 3 years
After calculating the future value of these payments, we add it to the initial amount in the bond account and calculate the future value of this total amount after another 3 years.
Step 2: Calculate the future value of the stock account The formula for the future value of a single amount is:
FV = PV * (1 + r)^n
where: PV = $82,000 (present value) r = 8% (annual interest rate) n = 6 years
Step 3: Calculate the total amount at retirement We add the future values of the bond and stock accounts to get the total amount at retirement.
Step 4: Calculate the annual withdrawal amount The formula for the annuity payment from a present amount is:
PMT = PV * r / [1 - (1 + r)^-n]
where: PV = total amount at retirement r = 2% (annual interest rate of the savings account) n = 15 years
This will give us the amount your auntie is able to withdraw each year during her retirement.
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