Answer:
10.4%
Step-by-step explanation:
To calculate the annual interest rate of the account, we can use the formula for compound interest:
A = P * (1 + r/n)^(n*t)
Where:
A = Final account balance ($21,000 in this case)
P = Principal amount ($15,000 in this case)
r = Annual interest rate (to be determined)
n = Number of times interest is compounded per year (quarterly compounding in this case)
t = Number of years (6 years in this case)
Plugging in the given values, the equation becomes:
$21,000 = $15,000 * (1 + r/4)^(4*6)
To solve for r, we need to rearrange the equation and isolate r:
(1 + r/4)^(24) = $21,000 / $15,000
(1 + r/4)^(24) = 1.4
Now, take the 24th root of both sides to isolate (1 + r/4):
1 + r/4 = (1.4)^(1/24)
1 + r/4 = 1.026
Subtract 1 from both sides and multiply by 4:
r = (1.026 - 1) * 4
r = 0.104 or 10.4%
Therefore, the annual interest rate of this account is 10.4%.