abhasjha wrote:An investor opened a money market account with a single deposit of $6000 on Dec. 31, 2001. The interest earned on the account was calculated and reinvested quarterly. The compound interest for the first 3 quarters of 2002 was $125, $130, and $145, respectively. If the investor made no deposits or withdrawals during the year, approximately what annual rate of interest must the account earn for the 4th quarter in order for the total interest earned on the account for the year to be 10 percent of the initial deposit?
A 3.1%
B 9.3%
C 10.0%
D 10.5%
E 12.5%
Total amount of interest that must be earned over the entire year = 10% of 6000 = 600.
Interest earned in the first 3 quarters = 125+130+145 = 400.
Interest that must be earned in the 4th quarter = 600-400 = 200.
Amount in the account at the end of the 3rd quarter = (principal) + (interest earned in the first 3 quarters) = 6000+400 = 6400.
We can PLUG IN THE ANSWERS, which represent the annual interest rate required to earn $200 in the 4th quarter.
Since the answer choices represent the ANNUAL interest rate, 1/4 of the implied interest will be earned in the 4th quarter.
Answer choice D: 10.5%
1/4 of (10.5% of 6400) = (1/4)(10.5/100)(6400) = (10.5)(16) = 168.
To earn $200 in the 4th quarter, a higher interest rate is required.
The correct answer is
E.
Last edited by
GMATGuruNY on Tue Jul 15, 2014 6:42 am, edited 2 times in total.
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