Question 2 of 14 (1 polity 1 Question Athenpt 1 of 1 Time Remainty ze29 MeriaKindal 1 2 3 4 5 6 7 8 9 10 11 12 Esato 13 Amy received a \( \$ 1300 \) bonus. She decided to invest it in a 2 -year certificate of deposit (CD) with an annual interest rate of \( 1.23 \% \) compounded quarterly. Answer the questions below. Do not round any intermediate computations, and round your final answers to the nearest cent. If nececcary refer to the list of financial formulas. (a) Assuming no withdrawals are made, how much money is in Amy's account after 2 years? \( \square \) \( \square \) (b) How much interest is earned on Amy's investment after 2 years? ©? \( \square \) Calculator

To calculate the amount in Amy's account after 2 years, 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). - \( r \) is the annual interest rate (decimal). - \( n \) is the number of times that interest is compounded per year. - \( t \) is the time the money is invested for in years. In Amy's case: - \( P = 1300 \) - \( r = 0.0123 \) - \( n = 4 \) (quarterly) - \( t = 2 \) Plugging in the values: \[ A = 1300 \left( 1 + \frac{0.0123}{4} \right)^{4 \times 2} = 1300 \left( 1 + 0.003075 \right)^{8} \] Calculating this gives: \[ A = 1300 \left( 1.003075 \right)^{8} \approx 1300 \times 1.025252 \approx 1332.43 \] So, Amy's account balance after 2 years is approximately \( \$1332.43 \). Now for the interest earned: \[ \text{Interest} = A - P = 1332.43 - 1300 = 32.43 \] Thus, the interest earned on Amy's investment after 2 years is approximately \( \$32.43 \). --- In the 19th century, financial instruments like certificates of deposit (CDs) began to become popular as a way for banks to attract deposits while providing investors with a safer, albeit lower, return on their investments. The concept of compounding interests became a hot topic as more individuals sought to grow their savings. Without today’s banking regulations, rates varied widely, but the basic principles of interest have remained. In today's digital age, investing in CDs is a great option for those looking to save for specific goals while still earning interest. It’s also relatively low-risk, making it suitable for conservative investors. For Amy, the CD is a perfect choice if she wants to ensure her bonus grows steadily without the volatility of stocks. Plus, it’s a straightforward way to save!