Independent solution

How to solve this Equation of Value Timing question

Setup

Setup

Choose time 18 as the single comparison date. Each of the seventeen deposits must be accumulated from its own deposit date, while each withdrawal must be moved to time 18.

v=1/1.05v=1/1.05

Model

Model

The deposits therefore contribute X times the sum of 1.05 through 1.05¹⁷. The four withdrawals occur at time 18 and the three preceding dates, producing 50,000(1 + v + v² + v³).

use time 18 as the comparison date\text{use time }18\text{ as the comparison date}

Compute

Compute

The displayed equation values both sides at time 18 with no missing or extra accumulation period, so choice D is the valid equation of value.

X∑k=1171.05k=50000(1+v+v2+v3)X\sum_{k=1}^{17}1.05^k=50000(1+v+v^2+v^3)

Answer

Answer

The calculation gives X ∑1.05 for equation of value timing, matching published choice D.

X∑k=1171.05k=50000(1+v+v2+v3)(D)\boxed{X\sum_{k=1}^{17}1.05^k=50000(1+v+v^2+v^3)\quad\text{(D)}}