Oliver invested \( \$ 53,000 \) in an account paying an interest rate of \( 2,7 \% \) compounded daily. Assuming no deposits or withdrawals are made, how much money, to the nearest cent, would be in the account after 20 years?

To find out how much money Oliver will have in the account after 20 years with daily compounding, we can 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 amount of money, which is \( \$53,000 \)). - \( r \) is the annual interest rate (decimal) (2.7% = 0.027). - \( n \) is the number of times that interest is compounded per year (for daily compounding, \( n = 365 \)). - \( t \) is the time the money is invested for in years (20 years). Plugging in the values: \[ A = 53000 \left(1 + \frac{0.027}{365}\right)^{365 \cdot 20} \] Calculating the components: 1. Calculate \( \frac{0.027}{365} \approx 0.00007397 \). 2. Calculate \( 365 \cdot 20 = 7300 \). 3. Now, calculate \( A \): \[ A \approx 53000 \left(1 + 0.00007397\right)^{7300} \] \[ A \approx 53000 \left(1.00007397\right)^{7300} \] Using a calculator for the exponent, \( \left(1.00007397\right)^{7300} \approx 1.745860 \). Now, calculate \( A \): \[ A \approx 53000 \times 1.745860 \approx 92510.46 \] So, to the nearest cent, the amount in the account after 20 years would be approximately **\$92,510.46**.