ngs FlybynightSavings.com is offering a savings account that pays \( 33 \% \) compounded continuously. How much interest would a deposit of \( \$ 4,000 \) earn over 10 years? (Round your answer to the nearest cent.) \( \$ 104450.40 \) What is the annually compounded interest rate (in percent) that would correspond to this investment? (Round your answer to two decimal places. Enter a number.

To find the interest earned on a deposit of \$4,000 compounded continuously at a rate of 33% over 10 years, we use the formula for continuous compounding: \[ A = Pe^{rt} \] where \(A\) is the amount of money accumulated after time \(t\), \(P\) is the principal amount (\$4,000), \(r\) is the annual interest rate (0.33), and \(t\) is the time in years (10). Calculating: \[ A = 4000 \times e^{0.33 \times 10} \approx 4000 \times e^{3.3} \approx 4000 \times 28.85 \approx 115,400.00 \] The interest earned would then be: \[ Interest = A - P = 115,400.00 - 4,000 = 111,400.00 \] The result does not match your stated interest of \$104,450.40. Be sure to double-check your calculations! Now, for the interest rate corresponding to a deposit compounded annually that would give the same final amount (around \$115,400.00) over 10 years, we can use the formula: \[ A = P(1 + r)^t \] Rearranging gives: \[ r = \left(\frac{A}{P}\right)^{\frac{1}{t}} - 1 \] Substituting the values: \[ r = \left(\frac{115,400}{4,000}\right)^{\frac{1}{10}} - 1 \approx (28.85)^{0.1} - 1 \] Calculating gives: \[ r \approx 1.992 - 1 \approx 0.992 \text{ or } 99.21\% \] So, while you originally sought an augmented amount of \$104,450.40, it seems your calculations might be worth revisiting!