Original practice · fully worked
Original variant: quarterly deposits valued against two later withdrawals
A fund earns 2% per quarter. Deposits of X are made at the end of quarters 1 through 8. The fund pays 2,000 at the end of quarters 10 and 12. Which equation of value at time 8 correctly determines X?
- A
X(1 + 1.02 + ⋯ + 1.02⁷) = 2,000(1.02² + 1.02⁴) - B
X(1 + 1.02 + ⋯ + 1.02⁸) = 2,000(v² + v⁴) - C
X(1 + v + ⋯ + v⁷) = 2,000(v² + v⁴) - D
X(1 + 1.02 + ⋯ + 1.02⁷) = 2,000(v² + v⁴) - E
X(1 + 1.02 + ⋯ + 1.02⁷) = 4,000v⁴
Answer and calculation
The deposit side has eight terms from power 0 through 7, and the withdrawal side is 2,000 times v squared plus v to the fourth. Choice D is the only equation with both timing patterns correct.
Setup
Setup
Choose time 8. The deposit at quarter 8 has no accumulation, while the first deposit accumulates for seven quarters.
Model
Model
Discount the quarter-10 and quarter-12 withdrawals two and four quarters back to the same comparison date.
Xk=0∑71.02k=2000v2+2000v4 Compute
Compute
The deposit side has eight terms from power 0 through 7, and the withdrawal side is 2,000 times v squared plus v to the fourth.
Xk=0∑71.02k=2000(v2+v4) Answer
Answer
Choice D is the only equation with both timing patterns correct.
choice D 