An investment of $200,000 in an instrument that returns an annual rate of...

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Mon Mar 30, 2020 2:37 am

e-GMAT

An investment of $200,000 in an instrument that returns an annual rate of r percent compounded semi-annually grows to $220,500 in one year. What is the value of r?

A. 5%
B. 5.125%
C. 10%
D. 10.25%
E. 20%

OA C

Given that the investment returns an annual rate of r percent compounded semi-annually, the semi-annual rate of return is r/2% and the no. of periods in one year for which the interest is calculated = 2*1 = 2 periods.

Thus, the question is simplified as:

An investment of $200,000 in an instrument put at a compounding rate of r/2 percent grows to $220,500 in two periods. What is the value of r?

A = P(1 + R/100)^n; where A = Amount after 2 periods = 220,500, P = principal = $200,000, R = r/2 and n = 2

220,500 = 200,000{1 + (r/2)/100}^2

220,500/220,500 = {1 + r/200}^2

441/400 = {1 + r/200}^2

√(441/400) = 1 + r/200

21/20 = 1 + r/200

21/20 – 1 = r/200

1/20 = r/200

r = 10%

The correct answer: C

Hope this helps!

-Jay
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AAPL wrote: ↑

Mon Mar 30, 2020 2:37 am

e-GMAT

An investment of $200,000 in an instrument that returns an annual rate of r percent compounded semi-annually grows to $220,500 in one year. What is the value of r?

A. 5%
B. 5.125%
C. 10%
D. 10.25%
E. 20%

OA C

Solution:

We can use the compound interest formula A = P(1 + r/n)^(nt) to solve this problem. Here, A = 220,500, P = 200,000, n = 2, and t = 1, and we need to solve for r:

220,500 = 200,000(1 + r/2)^(2 x 1)

1.1025 = (1 + r/2)^2

√1.1025 = √[(1 + r/2)^2]

1.05 = 1 + r/2

0.05 = r/2

r = 0.10 = 10%

Alternate solution:

We see that the total interest earned for the year is 220,500 - 200,000 = $20,500. Since the interest is compounded semi-annually, we can make an educated guess that the interest earned for the first half of the year is $10,000 and that for the second half of the year is $10,500 (because of the effect of compounding interest).

Since 10,000/200,000 = 0.05 = 5%, we see that the interest rate for half the year is 5%; thus,the annual interest rate is doubled to 10%.

Answer: C