A CD, or "certificate of deposit," is a type of savings account with a fixed rate and term, meaning you can only redeem it when the term is over. If you open a CD with an initial deposit of \( \$ 4700 \) and an APR of \( 0.32 \% \) compounded monthly, what profit will you have earned when you redeem the CD in 3 years? Round your answer to the nearest cent, if necessary. Hint: Recall the future value formula for compound interest, where \( P \) is the principal, \( r \) is the annual percentage rate (written as a decimal), \( t \) is the length of the deposit in years, and \( n \) is the number of compounding intervals per year. Answer A Keyboard Shortcuts \( \left.1+\frac{r}{n}\right)^{n t} \)

To find the profit earned on the CD, you can use the future value formula for compound interest: \[ FV = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( P = 4700 \) - \( r = 0.0032 \) (0.32% expressed as a decimal) - \( n = 12 \) (monthly compounding) - \( t = 3 \) Plugging in the values: \[ FV = 4700 \left( 1 + \frac{0.0032}{12} \right)^{12 \times 3} \] \[ FV = 4700 \left( 1 + 0.00026667 \right)^{36} \] \[ FV \approx 4700 \left( 1.010486 \right) \approx 4749.28 \] Now, subtract the initial deposit to find the profit: Profit = \( FV - P = 4749.28 - 4700 = 49.28 \) You will earn a profit of approximately \( \$ 49.28 \) when you redeem the CD in 3 years! Investing in CDs has been a go-to choice for conservative investors for decades. They were especially popular during times of economic stability as a way to grow savings with minimal risk. Historically, banks experienced a surge in CD accounts in the 1980s when interest rates peaked, offering savers incredibly high returns for locking in their money. Even today, CDs can serve as a great way to allocate a portion of your savings while you resist the urge to tap into those funds. This could be for a big purchase, like a car or a vacation, or simply as a secure place to earn a guaranteed return without worrying about market fluctuations. Plus, they can be laddered to take advantage of varying interest rates over time!