Ask AI: If you save $300 a month for 30 years (age 20 to 50) at 10% interest, how much money will you have?

To calculate the future value of a savings plan with regular monthly contributions and a fixed annual interest rate, we can use the future value of an annuity formula. Here, we are assuming the interest is compounded monthly. The formula for the future value of an annuity is: \[ FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right) \] Where: - \( FV \) is the future value of the annuity. - \( P \) is the monthly contribution ($300). - \( r \) is the monthly interest rate (annual rate divided by 12). So, \( 10\% \) per annum means \( \frac{10\%}{12} = 0.0083333 \) per month. - \( n \) is the total number of contributions (30 years × 12 months/year = 360 months). Plugging in the values: \[ FV = 300 \times \left( \frac{(1 + 0.0083333)^{360} - 1}{0.0083333} \right) \] First, calculate \( (1 + 0.0083333)^{360} \): \[ (1.0083333)^{360} \approx 198.392 \] Thus, the future value \( FV \) is: \[ FV \approx 300 \times \left( \frac{198.392 - 1}{0.0083333} \right) \] \[ FV \approx 300 \times \left( \frac{197.392}{0.0083333} \right) \] \[ FV \approx 300 \times 23691.74 \] \[ FV \approx 7,107,522 \] Therefore, if you save $300 a month for 30 years at an annual interest rate of 10%, compounded monthly, you would accumulate approximately $707,000.

You will have $1,125,094.76.