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

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

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New post Updated on: 29 Oct 2018, 23:27
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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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Originally posted by EgmatQuantExpert on 09 Oct 2018, 04:09.
Last edited by EgmatQuantExpert on 29 Oct 2018, 23:27, edited 1 time in total.
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Re: James invested $ 5000 in scheme A for 1 year at a simple annual ......  [#permalink]

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New post 09 Oct 2018, 05:10
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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Plan A interest: 5000*0.05= 250
Plan B interest: 10000*0.05=500 (for 1st 6 month)
And 10500*0.05=525( for next 6 months)

Positive difference =775

Answer:B


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

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New post 09 Oct 2018, 10:03
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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 ......  [#permalink]

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New post 11 Oct 2018, 04:36

Solution


Given:
    • James invested $5000 in scheme A for 1 year, and the simple annual interest rate is 5%
    • And, he also invested $10000 in scheme B for 1 year, and the annual interest rate is 10%, compounded semi-annually

To find:
    • Difference between the interests earned from scheme A and scheme B

Approach and Working:
In scheme A, the interest earned by James = \(5% of 5000 = \frac{5*5000}{100} = $250\)

In scheme B,
    • The interest earned by James in the first half of the year = (\(\frac{10}{2}\))% of 10000 = \(\frac{5*10000}{100}\) = $500
    • And, the interest earned by James in the latter half of the year = (\(\frac{10}{2}\))% of (10000 + 500) = \(\frac{5*10500}{100}\) = $525
    • Thus, the total interest earned for that year = $500 + $525 = $1025

Therefore, the positive difference in interests earned by James from schemes A and B = $1025 – $250 = $775

Hence, the correct answer is option B.

Answer: B

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Re: James invested $ 5000 in scheme A for 1 year at a simple annual ......   [#permalink] 11 Oct 2018, 04:36
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