Tom wants to buy a new truck in 2 years. He estimates the truck will cost approximately \( \$ 30,000 \) by then. How much should he invest now at \( 4 \% \) interest compoumded quarterly so that he will have enough to beys a new truct? Round to the nearest cent. OA. \( \$ 27,704,50 \) B. \( \$ 15,786.50 \) C. \( \$ 12,428.78 \) O. \( \$ 20,642.62 \)

To figure out how much Tom needs to invest now, 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 number of years the money is invested or borrowed. Setting \( A \) to \( 30,000 \), \( r \) to \( 0.04 \), \( n \) to \( 4 \), and \( t \) to \( 2 \): \[ 30,000 = P \left(1 + \frac{0.04}{4}\right)^{4 \times 2} \] Solving for \( P \): \[ P = \frac{30,000}{\left(1 + 0.01\right)^{8}} = \frac{30,000}{1.082856} \approx 27,704.50 \] So, Tom should invest approximately \( \$ 27,704.50 \). Here's a fun little historical twist: Did you know that the concept of compound interest has been around since ancient times? The Babylonians were already calculating it over 4,000 years ago! They understood that money can grow just by sitting there. Imagine them chatting over tablets of clay about their investments. Now let’s bring it to modern-day! Compounding can be your best friend when investing for future goals. By starting early and making regular contributions, not only can your money grow over time, but you might also find it easier to reach big purchases, like that dream truck! Setting a budget can help keep your eyes on the prize.