Questions: Arianna invests 5500 in a new savings account which earns 5.6% annual interest, compounded continuously. What will be the value of her investment after 7 years? Round to the nearest cent.

Solution Steps

We are given the following values for the investment:

• Principal amount \( P = 5500 \)
• Annual interest rate \( r = 5.6\% = 0.056 \)
• Time in years \( t = 7 \)

To find the future value \( A \) of the investment, we use the formula for continuous compounding: \[ A = Pe^{rt} \] Substituting the known values: \[ A = 5500 \cdot e^{0.056 \cdot 7} \]

First, we calculate the exponent: \[ rt = 0.056 \cdot 7 = 0.392 \] Now, we compute \( e^{0.392} \): \[ e^{0.392} \approx 1.478 \]

Now we can calculate \( A \): \[ A = 5500 \cdot 1.478 \approx 8139.6574 \] Rounding this to the nearest cent gives: \[ A \approx 8139.66 \]

Final Answer