Original practice · fully worked
Original variant: museum reserve with transferred interest
A museum places X into a noncompounding reserve at the beginning of each of six years. At each year-end, the reserve pays 10% simple interest on all principal then present into a separate account earning 6% annually. Find X if the two accounts together must hold 10,000 at the end of year 6.
- A
1,081.33 - B
1,141.74 - C
1,201.48 - D
1,261.22 - E
1,321.06
Answer and calculation
Principal and accumulated transfers provide a factor of 8.323063, so X = 1,201.48, choice C.
Setup
Setup
Track the reserve principal separately from the account that receives its annual interest.
V6=6X+k=1∑6(0.10kX)(1.06)6−k Model
Model
At year k, reserve principal is kX, so the transfer is 0.10kX and grows for six minus k years.
V6=8.32306275X Compute
Compute
The six principal deposits plus accumulated transfers produce 8.32306275X at year 6.
X=8.3230627510000=1201.4808 Answer
Answer
A deposit of 1,201.48 at each year-beginning meets the target, choice C.
X=1201.48(C) 