Jeff Miller

GMAT OFFICIAL GUIDE DS – A certain investment earned a fixed rate of 4 percent…

A certain investment earned a fixed rate of 4 percent…

Solution:

Since we are given information about compound interest, we can use the compound interest formula:

FV = PV(1 + r/n)^(nt), where

FV = future value

PV = present value

r = annual interest rate, expressed in decimal form

n = number of compounding periods per year

t = total number of years

Using the given information we have:

FV = PV(1+ 0.04/1)^(1 × t)

FV = PV(1.04)^t

So if we were to break down the value of the investment by year, we would have:

Value at beginning of year 1 = PV

Value at end of year 1 (or at beginning of year 2) = PV(1.04)

Value at end of year 2 (or at beginning of year 3) = PV(1.04)^2

Value at end of year 3 (or at beginning of year 4) = PV(1.04)^3

Value at end of year 4 (or at beginning of year 5) = PV(1.04)^4

Value at end of year 5 = PV(1.04)^5

Thus, the interest earned at the end of each year of the first three years would be:

Interest earned from year 1 = PV(1.04) – PV

Interest earned from year 2 = PV(1.04)^2 – PV(1.04)

Interest earned from year 3 = PV(1.04)^3 –PV(1.04)^2

We need to determine the difference between the interest earned during the third year and that during the first year. Thus:

[PV(1.04)^3 – PV(1.04)^2] – [PV(1.04) – PV]

We see that if we can determine the value of PV, we can answer the question.

Statement One Alone: 

The amount of the investment at the beginning of the second year was $4,160.00.

Since the value of the investment at the beginning at the second year is the same as the value of the investment at the end of the first year, we can say:

4,160.00 = PV(1.04)

We see that we can determine a value for PV. Thus, statement one alone is sufficient to answer the question. We can eliminate answer choices B, C, and E.

Statement Two Alone: 

The amount of the investment at the beginning of the third year was $4,326.40.

Since the value of the investment at the beginning at the third year is the same as the value of the investment at the end of the second year, we can say:

4,326.40 = PV(1.04)^2

We see that we can determine a value for PV. Thus, statement two alone is sufficient to answer the question.

Answer: D 

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