This Exam FM sample reference tests Savings and Withdrawal Equation. Solving the equation gives a monthly deposit of 240.38, which rounds to 240. The result agrees with the published answer key, choice C.
How to solve this Savings and Withdrawal Equation question
Setup
Setup
Convert 8% annual effective to its equivalent monthly rate. Savings deposits are made at the beginning of each month, and retirement withdrawals are made at the beginning of each year.
j=(1.08)1/12−1=0.006434
Model
Model
Value both streams at the retirement date. The four withdrawals form an annuity-due, while the 216 monthly deposits form an accumulated-value annuity-due and are moved to the same date.
25000a¨4∣0.08=Xs¨216∣j(1.08)−15
Compute
Compute
Solving the equation gives a monthly deposit of 240.38, which rounds to 240.
X=240.38
Answer
Answer
The calculation gives 240 for savings and withdrawal equation, matching published choice C.
X=240(C)
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These notes identify the calculation error associated with each wrong letter when that error is reproducible.
AChoice A (207) does not match the checked savings and withdrawal equation result (240); no distinct standard one-step error is identifiable.
BChoice B (223) does not match the checked savings and withdrawal equation result (240); no distinct standard one-step error is identifiable.
DChoice D (245) does not match the checked savings and withdrawal equation result (240); no distinct standard one-step error is identifiable.
EChoice E (260) does not match the checked savings and withdrawal equation result (240); no distinct standard one-step error is identifiable.
Original practice · fully worked
Original variant: monthly savings exchanged for retirement withdrawals
A saver deposits 400 at the beginning of each month for ten years into an account earning 6% nominal interest convertible monthly. At retirement, the balance is exchanged for eight equal annual withdrawals beginning immediately, valued at 4% annually. Calculate each withdrawal.
A 8,155.82
B 8,704.37
C 9,408.60
D 9,832.44
E 10,205.20
Variant answer in brief
The savings fund is 65879.50 and division by the eight-year annuity-due factor gives 9408.60. Each annual withdrawal is 9,408.60, selecting choice C.
Setup
Setup
Accumulate the 120 beginning-of-month deposits using a monthly annuity-due.
F=400s¨120∣0.005
Model
Model
At retirement, equate that balance to the value of eight beginning-of-year withdrawals at 4%.
F=Xa¨8∣0.04
Compute
Compute
The savings fund is 65879.50 and division by the eight-year annuity-due factor gives 9408.60.
F=65879.497416,X=9408.595123
Answer
Answer
Each annual withdrawal is 9,408.60, selecting choice C.
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