A bank offers a CD that pays a simple interest rate of \( 4.5 \% \). How much must you put in this CD now in order to have \( \$ 5000 \) for a graduation trip in 4 years? You must put \( \$ \square \) in this CD now in order to have \( \$ 5000 \) for a graduation trip in 4 years. (Round up to the nearest cent.)
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To find out how much you need to invest now, we can use the formula for simple interest: \[ A = P(1 + rt) \] 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). - \( t \) is the time the money is invested for in years. We want \( A = 5000 \), \( r = 0.045 \), and \( t = 4 \) years. Plugging in these values, we get: \[ 5000 = P(1 + 0.045 \times 4) \] \[ 5000 = P(1 + 0.18) \] \[ 5000 = P(1.18) \] Now, solving for \( P \): \[ P = \frac{5000}{1.18} \approx 4237.29 \] You must put \( \$ 4237.29 \) in this CD now in order to have \( \$ 5000 \) for a graduation trip in 4 years.