Alex deposited x dollars into a new account that earned 8

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pm; Followed by:23 members

Alex deposited x dollars into a new account that earned 8

by BTGmoderatorDC » Sat Jun 22, 2019 7:10 pm

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Alex deposited x dollars into a new account that earned 8 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ?

A. w/(1+1.08)
B. w/(1.08+1.16)
C. w/(1.16+1.24)
D. w/(1.08+1.08^2)
E. w/(1.08^2+1.08^2)

OA D

Source: Official Guide

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Source: Beat The GMAT — Problem Solving | Sat Jun 22, 2019 7:10 pm

swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

by swerve » Sun Jun 23, 2019 9:11 am

\(1.08(1.08x + x) = (1.08^2)x + 1.08x\)

The new total value obtained is equal to \(w\), we can set up the following equation:

\(w = (1.08^2)x + 1.08x\)

So, \(X\) in terms of \(w\)

\(w = x(1.08^2 + 1.08)\)

\(w/(1.08^2 + 1.08) = x\)

Therefore, __D__ is the correct option.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu Jun 27, 2019 5:32 pm

BTGmoderatorDC wrote:Alex deposited x dollars into a new account that earned 8 percent annual interest, compounded annually. One year later Alex deposited an additional x dollars into the account. If there were no other transactions and if the account contained w dollars at the end of two years, which of the following expresses x in terms of w ?

A. w/(1+1.08)
B. w/(1.08+1.16)
C. w/(1.16+1.24)
D. w/(1.08+1.08^2)
E. w/(1.08^2+1.08^2)

OA D

Source: Official Guide

We start by determining the new value of the x dollars Alex deposited into his account that earned 8 percent annual interest. At the end of the first year the amount of money in the account was 1.08x and then he added another x dollars to the account, so the account then had a total value of 1.08x + x dollars. The 1.08x + x dollars earned another 8 percent interest for the year. Thus, the total value of his account at the end of the second year is:

1.08(1.08x + x) = (1.08^2)x + 1.08x

Since the new total value is equal to w, we can set up the following equation:

w = (1.08^2)x + 1.08x

Now we must get x in terms of w.

w = x(1.08^2 + 1.08)

w/(1.08^2 + 1.08) = x

Answer: D

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