cccmom 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%
Interest earned for the first three quarters =
$125 + $130 + $145 =
$400GOAL: The total interest earned on the account for the year to be 10 percent of the initial deposit?
10% of
$6000 =
$600$600 -
$400 =
$200So, we want the investor to earn
$200 of interest during the 4th quarter.
After the first 3 quarters, the amount in the account =
$6000 +
$400 =
$6400What percent of
$6400 equals
$200?
To find out if we need to write
$200/
$6400 as a percent.
200/6400 = 2/64 = 1/31 = 3/93 ≈ 3.1%
So, to earn
$200 interest in the 4th quarter, we need a
QUARTERLY interest rate of about ≈ 3.1%
Since the question asks for the ANNUAL interest rate, we must multiply 3.1% by 4 to get 12.4%
Answer: E