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## A certain investment earned a fixed rate of 4 percent

tagged by: Brent@GMATPrepNow

This topic has 2 expert replies and 0 member replies
jjjinapinch Senior | Next Rank: 100 Posts
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#### A certain investment earned a fixed rate of 4 percent

Thu Jul 27, 2017 12:06 pm
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

Official Guide question

### GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
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Fri Jul 28, 2017 5:44 am
jjjinapinch wrote:
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

Official Guide question
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

Cheers,
Brent

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Rich.C@EMPOWERgmat.com Elite Legendary Member
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Fri Jul 28, 2017 11:20 am
Hi jjjinapinch,

This is a great 'concept' question - meaning that if you recognize the concept(s) involved, you don't have to do much (if any) math to get to the correct answer.

In this prompt, we're told that an investment earns a fixed 4% interest, compounded annually for 5 years. We're asked for the difference, in interest earnings, between the 3rd year and the 1st year.

To start, we don't know the initial investment. However, since we're compounding the interest each year, then we know that the interest will be 4% of whatever total amount is already there. Thus, we have a constant 'multiplier' (1.04) that we'll just keep multiplying year-after-year. This means that if we know ANY dollar figure at any point in the 5 year history, then we can figure out ALL of the other values (using either division - to move backwards, or multiplication - to move forwards).

1) The amount of the investment at the beginning of the second year was $4,160.00 With this Fact, we can move 'backwards' and 'forwards' as described above and get the necessary information to answer the question. Fact 1 is SUFFICIENT. 2) The amount of the investment at the beginning of the third year was$4,326.40

Just as in Fact 1 (above), we can move 'backwards' and 'forwards' as described and get the necessary information to answer the question.
Fact 2 is SUFFICIENT.

GMAT assassins aren't born, they're made,
Rich

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