# 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 **