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
Answer and calculation
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.
X=9408.60(C) Calculator reproduction
BA II Plus keystrokes
- 2nd CLR TVM; 120 N; 0.5 I/Y; 400 +/- PMT; 0 PV; 2nd PMT; 2nd SET; 2nd QUIT; CPT FV65879.50BGN mode for monthly deposits.
- 8 N; 4 I/Y; 65879.50 +/- PV; 0 FV; CPT PMT9408.60Keep BGN mode for immediate annual withdrawals.
