Questions: Consumer Mathematics Finding the future value and interest for an investment earning compound... The Carters are saving up to go on a family vacation in 5 years. They invest 2400 into an account with an annual interest rate of 1.49% compounded quarterly. Answer the questions below. Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas. (a) Assuming no withdrawals are made, how much money is in the Carters' account after 5 years? (b) How much interest is earned on the Carters' investment after 5 years?

Solution Steps

To calculate the future value \(A\) of an investment, we use the formula \(A = P(1 + \frac{r}{n})^{nt}\), where:

• \(P\) is the principal amount or the initial investment, which is $2400.
• \(r\) is the annual interest rate (in decimal), which is 0.0149.
• \(t\) is the time the money is invested for, in years, which is 5.
• \(n\) is the number of times the interest is compounded per year, which is 4. Substituting the given values into the formula, we get \(A = 2400 \times (1 + \frac{0.0149}{4})^{4\times5}\). After performing the calculations, the future value of the investment is approximately $2585.27.

The total interest earned can be calculated by subtracting the principal amount from the future value: \(\text{Total Interest} = A - P\). Substituting the calculated future value and the given principal amount, we get \(\text{Total Interest} = 2585.27 - 2400\). After performing the calculations, the total interest earned on the investment is approximately $185.27.

Final Answer: