Numeric 1 point Tessa deposited \( \$ 1,056.25 \) in a 4-year CD paying \( 6.01 \% \) compounded daily. How much more interest would she earn if the CD paid the same rate compounded continuously? Type your answer...

To find how much more interest Tessa would earn if the CD paid interest compounded continuously instead of daily, we can use the formulas for each method. 1. **Daily Compounding:** - Formula: \( A = P \left(1 + \frac{r}{n}\right)^{nt} \) - Where: - \( A \) = the amount of money accumulated after n years, including interest. - \( P \) = principal amount (initial deposit). - \( r \) = annual interest rate (decimal). - \( n \) = number of times interest is compounded per year. - \( t \) = number of years the money is invested or borrowed. Using \( P = 1056.25 \), \( r = 0.0601 \), \( n = 365 \), and \( t = 4 \): \[ A = 1056.25 \left(1 + \frac{0.0601}{365}\right)^{365 \times 4} \approx 1056.25 (1.2614) \approx 1334.87 \] - Interest earned = \( A - P = 1334.87 - 1056.25 = 278.62 \) 2. **Continuous Compounding:** - Formula: \( A = Pe^{rt} \) - Where \( e \) is the base of the natural logarithm, approximately equal to 2.71828. Using the same values: \[ A = 1056.25 e^{0.0601 \times 4} \approx 1056.25 e^{0.2404} \approx 1056.25 \times 1.2712 \approx 1346.85 \] - Interest earned = \( A - P = 1346.85 - 1056.25 = 290.60 \) Now, to find the difference in interest earned: \[ \text{Difference} = 290.60 - 278.62 \approx 11.98 \] Thus, Tessa would earn approximately **$11.98** more interest if the CD paid the same rate compounded continuously.