Problem Solving

AAPL wrote:e-GMAT

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

OA B.

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

AAPL wrote:e-GMAT

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