Original practice · fully worked
Original variant: compare two scholarship streams
At 10% effective annually, Scholarship A pays 300 at each year-end for five years. Scholarship B pays 200 at years 1 and 2, then 200 every year from year 6 onward. How much greater is the present value of B than the present value of A?
- A
351.71 - B
401.71 - C
451.71 - D
501.71 - E
551.71
Answer and calculation
The two present values are 1,137.24 and 1,588.95, so B exceeds A by 451.71, choice C.
Setup
Setup
Value the finite scholarship and the split stream separately at the common valuation date.
PA=300a5∣0.10=1137.2360 Model
Model
The later perpetuity has its value one period before its first payment, so discount that value five years.
PB=200a2∣0.10+200v5a∞∣0.10=1588.9501 Compute
Compute
Subtracting the five-payment annuity value from the split-stream value gives 451.7141.
PB−PA=1588.9501−1137.2360=451.7141 Answer
Answer
Scholarship B is worth 451.71 more at time zero, corresponding to choice C.
PB−PA=451.71(C) 