Suppose you invest \( \$ 150 \) a month for 5 years into an account earning \( 8 \% \) compounded monthly. After 5 years, you leave the money, without making additional deposits, in the account for another 30 years. How much will you have in the end?

To calculate your investment, we first find the future value of the investment after 5 years of monthly deposits using the future value of an annuity formula. The formula is: \[ FV = P \times \frac{(1 + r)^n - 1}{r} \] Where: - \( P = 150 \) (monthly investment) - \( r = \frac{0.08}{12} = 0.006667 \) (monthly interest rate) - \( n = 5 \times 12 = 60 \) (total number of deposits) Plugging in the values: \[ FV = 150 \times \frac{(1 + 0.006667)^{60} - 1}{0.006667} \] \[ FV = 150 \times \frac{(1.48985 - 1)}{0.006667} \approx 150 \times 73.491 \approx 11023.65 \] Now, after 5 years, the value is approximately \( \$ 11,023.65 \). Next, we let this amount sit in the account for another 30 years with no additional contributions, using the future value formula: \[ FV = P \times (1 + r)^n \] Where: - \( P = 11023.65 \) - \( r = 0.08/12 = 0.006667 \) - \( n = 30 \times 12 = 360 \) Calculating this gives: \[ FV = 11023.65 \times (1 + 0.006667)^{360} \] \[ FV = 11023.65 \times (8.893) \approx 98046.73 \] So, at the end of 35 years, you will have approximately \( \$ 98,046.73 \).