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
