After you've made these adjustments you can now work the problem using the periodic interest rate and total number of periods in your calculations. Try working the following example. You deposit \( \$ 6,000 \) today in an account that pays \( 29 \% \) interest per year with daily compounding. How much will you have in the account 10 years from today? Assume a 365 -day year. Round your answer to the nearest penny. Type your answer-

To calculate the future value of your deposit, we will use the formula for compound interest: \[ A = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( A \) is the amount of money accumulated after n years, including interest. - \( P \) is the principal amount (the initial deposit or investment). - \( r \) is the annual interest rate (decimal). - \( n \) is the number of times that interest is compounded per year. - \( t \) is the number of years the money is invested for. In this example: - \( P = 6000 \) - \( r = 0.29 \) (which is \( 29\% \) as a decimal) - \( n = 365 \) (daily compounding) - \( t = 10 \) Plugging these values into the formula: \[ A = 6000 \left(1 + \frac{0.29}{365}\right)^{365 \times 10} \] Calculating this gives: 1. Calculate \( \frac{0.29}{365} \approx 0.0007945205 \) 2. Then calculate \( 1 + 0.0007945205 \approx 1.0007945205 \) 3. Raise this to the power of \( 3650 \) (which is \( 365 \times 10 \)): \( (1.0007945205)^{3650} \approx 12.11283184 \) 4. Finally, multiply by \( 6000 \): \( A \approx 6000 \times 12.11283184 \approx 72676.99 \) So after 10 years, you will have approximately **$72,676.99** in the account.