James invested $5000 in scheme A for 1 year at a simple

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AAPL: Moderator; Posts: 2599; Joined: Sun Oct 29, 2017 2:08 pm; Followed by:2 members

James invested $5000 in scheme A for 1 year at a simple

by AAPL » Tue Oct 09, 2018 4:30 am

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James invested $5000 in scheme A for 1 year at a simple annual interest rate of 5% and invested another $10000 in scheme B for one year at an annual interest rate of 10% compounded semi-annually. What is the positive difference between the interest earned by James from scheme A and scheme B?

A. 250
B. 775
C. 1025
D. 1750
E. 2000

OA B.

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Source: Beat The GMAT — Problem Solving | Tue Oct 09, 2018 4:30 am

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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

by Brent@GMATPrepNow » Tue Oct 09, 2018 4:55 am

AAPL wrote:e-GMAT

James invested $5000 in scheme A for 1 year at a simple annual interest rate of 5% and invested another $10000 in scheme B for one year at an annual interest rate of 10% compounded semi-annually. What is the positive difference between the interest earned by James from scheme A and scheme B?

A. 250
B. 775
C. 1025
D. 1750
E. 2000

OA B.

Scheme A
Interest = 5% of $5,000 = $250

Scheme B
10% interest compounded semi-annually means that the interest is compounded 2 times (in 1 year) at a rate of 5% each time
One option is to apply the compound interest formula, but since we're only compounding the interest twice, it may be faster to just perform those 2 calculations.

After 6 months, the interest = 5% of $10,000 = $500
So, the value of the investment = $10,000 + $500 = $10,500

After 12 months, the interest = 5% of $10,500 = $525
So, the value of the investment = $10,500 + $525= $11,025

So, the accumulated interest = $11,025 - $10,000 = $1,025

What is the positive difference between the interest earned by James from scheme A and scheme B?
Difference = $1,025 - $250 = $775

Answer: B

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8083; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Fri Oct 12, 2018 6:54 am

AAPL wrote:e-GMAT

James invested $5000 in scheme A for 1 year at a simple annual interest rate of 5% and invested another $10000 in scheme B for one year at an annual interest rate of 10% compounded semi-annually. What is the positive difference between the interest earned by James from scheme A and scheme B?

A. 250
B. 775
C. 1025
D. 1750
E. 2000

For scheme A, the amount of interest earned is 5000 x 0.05 = 250 dollars.

For scheme B, since the interest is compounded twice a year, the annual interest rate of 10% is halved for each 6-month compounding period.

10,000 x 0.05 = 500 dollars are earned in the first 6 months. Thus, the principal is now 10,500.

10,500 x 0.05 = 525 dollars are earned in the last 6 months.

So a total amount of interest earned is 1,025 dollars.

So the difference is 1,025 - 250 = 775 dollars.

Answer: B

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