Question 1
Multiple ChoiceMs. Hofstadter plans to spend $90,000 per year for 20 years in retirement. She plans to fund this by making end-of-year deposits of $7,200 annually during her working years. She expects to earn an annual return of 5.5%, compounded annually, on all investments. What is the minimum number of deposits she needs to make to achieve her retirement goal?
Explanation
Step 1: Calculate the present value (PV) of the retirement withdrawals.
This is an ordinary annuity:
PMT = 90,000
N = 20
I/Y = 5.5
FV = 0
Solve for PV:
On BA II Plus:
[2nd] [CLR TVM]
N = 20
I/Y = 5.5
PMT = -90,000
FV = 0
CPT → PV ≈ 1,123,752.18
Step 2: Use this PV as the FV of the working years savings.
We solve for N given:
FV = 1,123,752.18
PMT = -7,200
I/Y = 5.5
PV = 0
On BA II Plus:
[2nd] [CLR TVM]
PMT = -7,200
I/Y = 5.5
PV = 0
FV = 1,123,752.18
CPT → N ≈ 46.0
She will need to make 46 deposits to meet her goal.