enigma123 wrote:
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%
Solution:We can use the compound interest formula, where A is the final value of the investment, P is the original principal, r is the annual interest rate (as a decimal), n is the number of compounding periods per year, and t is the number of years:
A = P(1 + r/n)^(nt)
Here, we are given A = 76,662.25, P = 61,293, n = 4 and t = 5. We need to find r:
76,662.25 = 61,293(1 + r/4)^(4*5)
1.25075 = (1 + r/4)^20
^20√1.25075 = 1 + r/4
1.01125 = 1 + r/4
0.01125 = r/4
r = 0.045 = 4.5%
Alternate Solution:The answer choices vary greatly, which is an indication that the interest rate can be approximated without using a calculator.
We see that 76,600 - 61,300 = $15,300 in interest was earned during the 5-year period. This is an average of a bit more than $3,000 per year in interest.
As a percentage of the original amount invested, we see that the yield is about 3,000/60,000, or 1/20, which is 5% per year. Of the answer choices, this is very close to 4.5% per year, and no other answer choice is a viable candidate.
Answer: B _________________
★
★
★
★
★
250 REVIEWS
5-STAR RATED ONLINE GMAT QUANT SELF STUDY COURSE
NOW WITH GMAT VERBAL (BETA)
See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews