BTGmoderatorDC wrote: ↑Mon Apr 20, 2020 6:03 pm
Diana invested $61,293 in an account with a fixed annual percent of interest, compounding quarterly. At the end of five full years, she had $76,662.25 in principal plus interest. Approximately what was the annual percent rate of interest for this account?
A. 1.2%
B. 4.5%
C. 10%
D. 18%
E. 25.2%
OA
B
Source: Magoosh
This question involves ugli numbers. If we go with the traditional method for solving, we would need a calculator. However, in the GMAT, a calculator is not allowed.
Anyway, let's understand how it would have been solved, applying the traditional method.
The formula for CI is as follows.
A = P(1 + r/100)^n;
A = Amount after 5 years = 76,662;
P = Principal = 61,293
r = Quarterly rate of interest. Thus, the answer would be 4r, the annual rate of interest
n = No. of periods = 4*5 = 20
76,662 = 61,293(1 + r/100)^20
(76,662/61,293)^(1/20) = 1 + r/100;
From this point, we are helpless.
Let's do this problem with another approach.
So, Diana earned an interest of 76,662 – 61,293 = ~15,000 earned in 5 years
=> 15,000/5 = 3,000 in a year
Simple rate of interest per annum = 3,000/60,000 = ~5%
However, 5% must be an incorrect answer as this is a CI question and the rate of interest must be less than 5%. The closest is 4.5%. Option A 1.2% is far too less.
The correct answer:
B
Hope this helps!
-Jay
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