How much should you deposit at the end of each month into an investment account that pays \( 6 \% \) compounded monthly to have \( \$ 2 \) million when you retire in 41 years? How much of the \( \$ 2 \) million comes from interest? (i) Click the icon to view some finance formulas.

To accumulate \( \$ 2 \) million in 41 years with a monthly investment in an account paying \( 6\% \) interest compounded monthly, you’ll want to use the future value of an annuity formula: \[ FV = P \times \frac{(1 + r)^n - 1}{r} \] Where: - \( FV \) is the future value (2,000,000) - \( P \) is the monthly deposit - \( r \) is the monthly interest rate (0.06/12 = 0.005) - \( n \) is the total number of deposits (41*12 = 492) Rearranging the formula to solve for \( P \): \[ P = \frac{FV \times r}{(1 + r)^n - 1} \] Plugging in the numbers yields: \[ P = \frac{2,000,000 \times 0.005}{(1 + 0.005)^{492} - 1} \approx 1,393.34 \] So, you should deposit approximately \( \$ 1,393.34 \) each month. Now, let’s find the total contributions and how much comes from interest. Over 41 years, your total contributions will be: \[ \text{Total contributions} = P \times n = 1,393.34 \times 492 \approx 685,009.68 \] Thus, the amount coming from interest will be: \[ \text{Interest} = FV - \text{Total contributions} = 2,000,000 - 685,009.68 \approx 1,314,990.32 \] In summary, you’ll be contributing about \( \$ 685,009.68 \) over the 41 years, and the interest earned will total approximately \( \$ 1,314,990.32 \). Now, that’s some serious money magic! Thinking about your financial future? It’s all about consistency and letting compound interest work for you! Regular monthly deposits can really add up over time, showcasing how earlier investments can lead to greater gains thanks to the wonder of compounding. Keeping track of your progress and adjusting as needed can help you hit your targets even faster!