To find the annual interest rate, we can use the formula for compound interest, which relates the present value (PV), future value (FV), interest rate (r), and time (t):
\[ FV = PV \times (1 + r)^t \]
In this case:
- \(FV = 3,792.00\)
- \(PV = 2,417.00\)
- \(t = 8.00\)
We need to solve for \(r\). Rearranging the equation gives us:
\[ (1 + r)^t = \frac{FV}{PV} \]
Substituting the known values:
\[ (1 + r)^8 = \frac{3,792.00}{2,417.00} \]
Calculating the right side:
\[ \frac{3,792.00}{2,417.00} \approx 1.5706 \]
Now, we need to take the eighth root of both sides to solve for \(1 + r\):
\[ 1 + r = (1.5706)^{\frac{1}{8}} \]
Calculating the eighth root:
\[ 1 + r \approx 1.0614 \]
Now, subtract 1 to find \(r\):
\[ r \approx 1.0614 - 1 = 0.0614 \]
To convert \(r\) to a percentage:
\[ r \approx 0.0614 \times 100 \approx 6.14% \]
Thus, the account earned approximately 6.14% per year.
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