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

Question

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.

B.

C.

D.

E.

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

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MikeScarn · Answer

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

Abhishek009 · Answer

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)

BrentGMATPrepNow · Answer

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

ScottTargetTestPrep · Answer

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

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