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

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James invested $5000 in scheme A for 1 year at a simple annual interes  [#permalink]

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New post 27 Aug 2018, 03:43
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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]

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New post 27 Aug 2018, 05:11
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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

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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
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Re: James invested $5000 in scheme A for 1 year at a simple annual interes  [#permalink]

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New post 27 Aug 2018, 07:11
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]

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New post 09 Oct 2018, 05:59
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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
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

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Re: James invested $5000 in scheme A for 1 year at a simple annual interes  [#permalink]

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New post 12 Oct 2018, 07:58
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
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Re: James invested $5000 in scheme A for 1 year at a simple annual interes   [#permalink] 12 Oct 2018, 07:58
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