You invest $25/month at a rate of 3.25% APR compounded monthly for 30 years.

1 answer

To calculate the future value of an investment where you contribute a fixed amount monthly, you can use the formula for the future value of a series of cash flows (an annuity). The formula is:

\[ FV = P \times \frac{(1 + r)^n - 1}{r} \]

Where:

  • \( FV \) = future value of the investment
  • \( P \) = amount contributed each period (monthly contribution)
  • \( r \) = interest rate per period (monthly interest rate)
  • \( n \) = total number of contributions (number of periods)

Given:

  • Monthly contribution, \( P = 25 \)
  • Annual interest rate, \( APR = 3.25% \) (0.0325 as a decimal)
  • Monthly interest rate, \( r = \frac{0.0325}{12} = 0.00270833 \)
  • Investment duration, 30 years, which means total months, \( n = 30 \times 12 = 360 \)

Now substituting these values into the formula:

  1. Calculate the monthly interest rate: \[ r = \frac{0.0325}{12} = 0.00270833 \]

  2. Calculate the total number of contributions (months): \[ n = 30 \times 12 = 360 \]

  3. Plug the values into the future value formula: \[ FV = 25 \times \frac{(1 + 0.00270833)^{360} - 1}{0.00270833} \]

  4. Calculate \( (1 + 0.00270833)^{360} \): \[ (1 + 0.00270833)^{360} \approx 2.63925 \]

  5. Now substitute this back into the future value formula: \[ FV = 25 \times \frac{2.63925 - 1}{0.00270833} \]

  6. Calculate the future value: \[ FV = 25 \times \frac{1.63925}{0.00270833} \approx 25 \times 604.55598 \approx 15113.90 \]

Thus, the future value of your investment after 30 years, making monthly contributions of $25 at an interest rate of 3.25% compounded monthly, would be approximately $15,113.90.