Questions: Find the interest rate for a 9500 deposit accumulating to 11,650, compounded annually for 7 years. The interest rate is %. (Do not round until the final

Solution Steps

To find the interest rate for a deposit that grows from $9,500 to $11,650 over 7 years with annual compounding, we can use the formula for compound interest: \( A = P(1 + r)^n \), where \( A \) is the final amount, \( P \) is the principal amount, \( r \) is the interest rate, and \( n \) is the number of years. We need to solve for \( r \).

1. Substitute the given values into the compound interest formula.
2. Rearrange the formula to solve for \( r \).
3. Use Python to calculate the interest rate.

We are given:

• Principal amount \( P = 9500 \)
• Final amount \( A = 11650 \)
• Number of years \( n = 7 \)

The compound interest formula is given by: \[ A = P(1 + r)^n \] Substituting the known values: \[ 11650 = 9500(1 + r)^7 \]

To isolate \( r \), we first divide both sides by \( 9500 \): \[ \frac{11650}{9500} = (1 + r)^7 \] Calculating the left side: \[ \frac{11650}{9500} \approx 1.2252631578947368 \] Now, we take the seventh root: \[ 1 + r = \left(1.2252631578947368\right)^{\frac{1}{7}} \] Subtracting 1 gives us \( r \): \[ r \approx 0.029573780879535994 \]

To express \( r \) as a percentage: \[ \text{Interest Rate} = r \times 100 \approx 2.9574\% \]

Final Answer