Data Sufficiency

BTGmoderatorLU wrote: ↑

Sun Apr 23, 2023 3:28 pm

Source: Official Guide

A certain investment earned a fixed rate of 4 percent interest per year, compounded annually, for five years. The interest earned for the third year of the investment was how many dollars greater than that for the first year?

1) The amount of the investment at the beginning of the second year was $4,160.00.
2) The amount of the investment at the beginning of the third year was $4,326.40.

The OA is D

Target question: The interest earned for the third year of the investment was how many dollars greater than that for the first year?

Given: A certain investment earned a fixed rate of 4 percent interest per year, compounded annually, for five years.
So, we have:
Let P = the initial investment
After 1 year, the value of the investment = P(1.04)
After 2 years, the value of the investment = P(1.04)^2
After 3 years, the value of the investment = P(1.04)^3
After 4 years, the value of the investment = P(1.04)^4
After 5 years, the value of the investment = P(1.04)^5

Statement 1: The amount of the investment at the beginning of the second year was $4,160.00
The value of the investment at the BEGINNING of the second year is the same as value of the investment at the END of the first year
So, we can write: P(1.04) = $4,160.00
Since we COULD solve this question for P, we COULD determine the value of the investment for each of the 5 years, which means we COULD answer the target question with certainty.
As such, statement 1 is SUFFICIENT

Statement 2: The amount of the investment at the beginning of the third year was $4,326.40
The value of the investment at the BEGINNING of the third year is the same as value of the investment at the END of the second year
So, we can write: P(1.04)^2 = $4,326.40
Since we COULD solve this question for P, we COULD determine the value of the investment for each of the 5 years, which means we COULD answer the target question with certainty.
As such, statement 2 is SUFFICIENT

Answer: D