To calculate the final balance of an investment with monthly contributions compounded monthly, you can use the future value of a series formula:
\[ FV = P \times \frac{(1 + r)^n - 1}{r} \]
Where:
- \( FV \) is the future value of the investment
- \( P \) is the amount of each payment (monthly contribution)
- \( r \) is the monthly interest rate (annual rate divided by 12)
- \( n \) is the total number of contributions (months)
In this case:
- Monthly contribution (\( P \)) = $25
- Annual interest rate = 3.25% = 0.0325
- Monthly interest rate (\( r \)) = 0.0325 / 12 = 0.00270833
- Total months (\( n \)) = 30 years × 12 months/year = 360 months
Now we can plug in the values into the formula:
\[ FV = 25 \times \frac{(1 + 0.00270833)^{360} - 1}{0.00270833} \]
Now, we calculate \( (1 + 0.00270833)^{360} \):
\[ (1 + 0.00270833)^{360} \approx 2.848230 \]
Now substituting this value back into the formula:
\[ FV = 25 \times \frac{2.848230 - 1}{0.00270833} \] \[ FV = 25 \times \frac{1.848230}{0.00270833} \] \[ FV = 25 \times 682.5455344 \approx 17136.14 \]
So the final balance after 30 years will be approximately $17,136.14.
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