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27 Aug 2018, 04:11
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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: $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

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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, 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)
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Re: James invested $5000 in scheme A for 1 year at a simple annual interes [#permalink] ### Show Tags 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 Answer: B Cheers, Brent _________________ Test confidently with gmatprepnow.com Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 4915 Location: United States (CA) Re: James invested$5000 in scheme A for 1 year at a simple annual interes  [#permalink]

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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.

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