Roger's hedge fund is taking x dollars and investing in bonds that yield r percent in simple interest. The amount of interest earned over 2 years is $1000. In terms of x, what dollar amount invested will yield $4000 over 5 years, assuming the bond's yield remains the same?
A. x
B. 2x/3
C. 2x
D. 4x/3
E. 8x/5
The OA is E.
Is there a strategic approach to solve this question? Can anyone help, please? Thanks!
Roger's edge fund is taking x dollars and investing in bonds
This topic has expert replies
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Roger's hedge fund is taking x dollars and investing in bonds that yield r percent in simple interest. The amount of interest earned over 2 years is $1000.AAPL wrote:Roger's hedge fund is taking x dollars and investing in bonds that yield r percent in simple interest. The amount of interest earned over 2 years is $1000. In terms of x, what dollar amount invested will yield $4000 over 5 years, assuming the bond's yield remains the same?
A. x
B. 2x/3
C. 2x
D. 4x/3
E. 8x/5
So, the original investment of x dollars results in $500 interest EACH YEAR
In terms of x, what dollar amount invested will yield $4000 over 5 years?
$4000 over 5 years is the same as $800 interest EACH YEAR
We can solve this question with equivalent ratios
We'll compare investment/interest EACH YEAR
Let y = the investment needed to earn $800 interest EACH YEAR
We get: x/500 = y/800
Cross multiply: 800x = 500y
Divide both sides by 500 to get: 800x/500 = y
Simplify to get: 8x/5 = y
Answer: E
Cheers,
Brent
GMAT/MBA Expert
- Jeff@TargetTestPrep
- GMAT Instructor
- Posts: 1462
- Joined: Thu Apr 09, 2015 9:34 am
- Location: New York, NY
- Thanked: 39 times
- Followed by:22 members
We use the simple interest formula: interest = principal x rate x time. Letting x = the principal and expressing the interest rate as a decimal, we can create the equation:AAPL wrote:Roger's hedge fund is taking x dollars and investing in bonds that yield r percent in simple interest. The amount of interest earned over 2 years is $1000. In terms of x, what dollar amount invested will yield $4000 over 5 years, assuming the bond's yield remains the same?
A. x
B. 2x/3
C. 2x
D. 4x/3
E. 8x/5
(x)(r/100)(2) = 1000
xr = 50,000
r = 50,000/x
For a 5-year period,, letting p = the new principal, the amount of interest earned will be:
(p)[(50,000/x)/100](5) = 4000
(p)(500/x) = 800
p = 800/(500/x)
p = 800x/500 = 8x/5
Alternate Solution:
Let's first find the interest paid to x dollars over a period of 5 years. Since 5 is 2.5 times 2, the interest paid to x dollars in 5 years should also be 2.5 times the interest paid to x dollars in 2 years; i.e. 2500 dollars.
Now, let's denote the amount required to earn 4000 dollars in 5 years by y and set up a simple proportion:
x/2500 = y/4000
y = 4000x/2500 = 8x/5
Answer: E
Jeffrey Miller
Head of GMAT Instruction
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews