To calculate the future value of a savings account with monthly contributions and compound interest, 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 monthly contribution
- \( r \) is the monthly interest rate
- \( n \) is the total number of contributions
In your case:
- \( P = 1583 \)
- The annual interest rate is 4.5%, so the monthly interest rate \( r = \frac{4.5%}{12} = \frac{0.045}{12} \approx 0.00375 \)
- Since you are contributing monthly for a year, \( n = 12 \)
Now, plug the values into the formula:
\[ FV = 1583 \times \frac{(1 + 0.00375)^{12} - 1}{0.00375} \]
Calculate \( (1 + 0.00375)^{12} \):
\[ (1 + 0.00375)^{12} \approx 1.046022 \]
Now plug it back into the formula:
\[ FV = 1583 \times \frac{1.046022 - 1}{0.00375} \] \[ FV = 1583 \times \frac{0.046022}{0.00375} \] \[ FV = 1583 \times 12.97253 \approx 20466.22 \]
Therefore, after one year of saving $1583 per month in an account with 4.5% compound interest compounded monthly, you will have approximately $20,466.22.