Original practice · fully worked
Original variant: first grant in an increasing cultural-fund schedule
A cultural fund pays X immediately, 2X one year later, and continues increasing by X annually through the tenth payment. At 5% effective annually, the stream is worth 10,000. Determine X.
- A
200.00 - B
225.00 - C
241.88 - D
260.00 - E
280.00
Answer and calculation
The ten-payment increasing annuity-due factor is 41.34247, so X = 241.88, choice C.
Setup
Setup
Payment k equals kX and occurs at time k minus one because the first grant is immediate.
10000=Xk=1∑10kvk−1,v=1/1.05 Model
Model
Factor out X and evaluate the ten-term time-indexed discount sum.
k=1∑10kvk−1=41.3424719 Compute
Compute
That factor is 41.3424719, making the base payment 241.8820.
X=10000/41.3424719=241.8820 Answer
Answer
The first grant is 241.88, which is choice C.
X=241.88(C) 