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27 Aug 2018, 02:43
00:00

Difficulty:

45% (medium)

Question Stats:

68% (01:29) correct 32% (02:00) wrong based on 90 sessions

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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

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Re: James invested $5000 in scheme A for 1 year at a simple annual interes [#permalink] ### Show Tags 27 Aug 2018, 04:11 1 EgmatQuantExpert wrote: 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 To read all our articles: Must read articles to reach Q51 Scheme A:$5,000 at 5% simple annual interest

5,000 * .05 * 1 = 5250 ----> $250 of interest Scheme B:$10,000 at 10% compounded semi annually

10,000(1 + $$\frac{.1}{2}$$)$$^2$$ --------> 10,000(1.05)$$^2$$ --------> 10,000(1.1025) = 11,025

$11,025 ----------->$1,025 of interest

Positive difference between the interest earned by Scheme A vs Scheme B

$1,025 -$250 = $775 Answer: B _________________ Would I rather be feared or loved? Easy. Both. I want people to be afraid of how much they love me. How to sort questions by Topic, Difficulty, and Source: https://gmatclub.com/forum/search.php?view=search_tags Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 4220 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: James invested$5000 in scheme A for 1 year at a simple annual interes  [#permalink]

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27 Aug 2018, 06:11
EgmatQuantExpert wrote:
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

$$Amount_{Si} = 5000 + \frac{5000*5*1}{100}$$

So, $$Amount_{Si} = 5250$$

$$Amount_{Ci} = 5000( 1 + \frac{10}{200})^{2}$$

So, $$Amount_{Ci} = 11025.00$$

So, the required difference is $1,025 -$250 = $775 , Answer must be (B) _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) CEO Joined: 11 Sep 2015 Posts: 3122 Location: Canada Re: James invested$5000 in scheme A for 1 year at a simple annual interes  [#permalink]

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09 Oct 2018, 04:59
Top Contributor
EgmatQuantExpert wrote:
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

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

Cheers,
Brent
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Re: James invested $5000 in scheme A for 1 year at a simple annual interes [#permalink] ### Show Tags 12 Oct 2018, 06:58 EgmatQuantExpert wrote: 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 _________________ Scott Woodbury-Stewart Founder and CEO GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Re: James invested$5000 in scheme A for 1 year at a simple annual interes &nbs [#permalink] 12 Oct 2018, 06:58
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