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. \(\dfrac{w}{1+1.08}\)
B. \(\dfrac{w}{1.08+1.16}\)
C. \(\dfrac{w}{1.16+1.24}\)
D. \(\dfrac{w}{1.08+1.08^2}\)
E. \(\dfrac{w}{1.08^2+1.08^2}\)
Answer: D
Source: Official Guide
Alex deposited \(x\) dollars into a new account that earned \(8\) percent annual interest, compounded annually. One year
This topic has expert replies
-
- Legendary Member
- Posts: 1622
- Joined: Thu Mar 01, 2018 7:22 am
- Followed by:2 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
GMAT/MBA Expert
- Ian Stewart
- GMAT Instructor
- Posts: 2621
- Joined: Mon Jun 02, 2008 3:17 am
- Location: Montreal
- Thanked: 1090 times
- Followed by:355 members
- GMAT Score:780
In the first year, the initial deposit of $x earns 8% interest, so after one year, the account holds 1.08x dollars.
Then an additional $x is deposited in the account, so the account now contains 1.08x + x = x(1.08 + 1) dollars.
This amount now earns 8% interest over the second year, so at the end of two years, the account holds (1.08)(x)(1.08 + 1) dollars. Since this amount is w, we can solve the following for x:
w = (1.08)(x)(1.08 + 1)
x = w/[(1.08)(1.08 + 1)]
x = w/(1.08^2 + 1.08)
and the answer is D.
Then an additional $x is deposited in the account, so the account now contains 1.08x + x = x(1.08 + 1) dollars.
This amount now earns 8% interest over the second year, so at the end of two years, the account holds (1.08)(x)(1.08 + 1) dollars. Since this amount is w, we can solve the following for x:
w = (1.08)(x)(1.08 + 1)
x = w/[(1.08)(1.08 + 1)]
x = w/(1.08^2 + 1.08)
and the answer is D.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
ianstewartgmat.com
ianstewartgmat.com