How much should you deposit at the end of each month into an investment account that pays \( 9 \% \) compounded monthly to have \( \$ 1 \) million when you retire in 45 years? How much of the \( \$ 1 \) million comes from interest? Click the icon to view some finance formulas. In order to have \( \$ 1 \) million in 45 years, you should deposit \( \$ \square \) each month. (Round up to the nearest dollar.)
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To find out how much you need to deposit each month, we can use the future value of an annuity formula: \[ FV = P \times \frac{(1 + r)^n - 1}{r} \] Where: - \( FV = \$1,000,000 \) - \( r = \frac{0.09}{12} = 0.0075 \) (monthly interest rate) - \( n = 45 \times 12 = 540 \) (total number of deposits) Rearranging to find \( P \): \[ P = \frac{FV \times r}{(1 + r)^n - 1} \] Plugging in the values, you’ll find that \( P \) is approximately \( \$1,206 \). Now, to find how much of the \$1 million comes from interest, calculate the total amount deposited: Total deposits = \( P \times n = 1,206 \times 540 = \$651,240 \). Subtract this from the total future value to find the interest: Interest = Total Future Value - Total Deposits = \( 1,000,000 - 651,240 = \$348,760 \). So, you should deposit approximately \( \$1,206 \) each month, and about \( \$348,760 \) comes from interest.