For her 1st birthday Adriana's parents invested \( \$ 8,000.00 \) in an 15 -year certificate for her that pays \( 9 \% \) compounded quarterly. How much is the certificate worth on Adriana's 16 birthday? Round value to the nearest cent. The certificate will be worth \( \$ \)

To calculate the future value of the investment, you'll 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 investment, which is \( \$ 8,000.00 \)). - \( r \) is the annual interest rate (decimal) (9% or 0.09). - \( n \) is the number of times that interest is compounded per year (quarterly means \( n = 4 \)). - \( t \) is the time the money is invested for in years (15 years). Plugging in the values, we get: \[ A = 8000 \left(1 + \frac{0.09}{4}\right)^{4 \times 15} \] Calculating that step by step: 1. \( \frac{0.09}{4} = 0.0225 \) 2. \( 4 \times 15 = 60 \) 3. \( A = 8000 \left(1 + 0.0225\right)^{60} \) 4. \( A = 8000 \left(1.0225\right)^{60} \) 5. \( A = 8000 \times 4.454 \) (approximately) 6. \( A \approx 35,632.00 \) Thus, rounding to the nearest cent, the certificate will be worth \( \$ 35,632.00 \) on Adriana's 16th birthday. --- If you'd like to learn more about certificates of deposit (CDs) or how investments are compounded over time, let me know! I'm here to help you explore these financial concepts!