\( t=\begin{array}{c}\text { Total Balanee }=3,000,000 \\ 3,000,000 \times \frac{0.05}{12} \\ {\left[\left(\left(1+\frac{0.05}{12}\right)^{(1260)}-1\right]\right.}\end{array} \)

It looks like you're trying to calculate the future value of an investment or savings account using the formula for compound interest. However, the expression you've provided seems to be incomplete or incorrectly formatted. To clarify, the formula for the future value \( FV \) of an investment compounded monthly is given by: \[ FV = P \left(1 + \frac{r}{n}\right)^{nt} \] Where: - \( P \) is the principal amount (initial investment), - \( r \) is the annual interest rate (in decimal), - \( n \) is the number of times that interest is compounded per year, - \( t \) is the number of years the money is invested or borrowed. From your input, it seems you have: - Total Balance \( P = 3,000,000 \) - Annual interest rate \( r = 0.05 \) (5%) - Compounding frequency \( n = 12 \) (monthly) - The exponent \( nt \) appears to be \( 1260 \), which suggests \( t \) might be in months. To find \( t \) in years, we can convert months to years: \[ t = \frac{1260}{12} = 105 \text{ years} \] Now, substituting these values into the future value formula: \[ FV = 3,000,000 \left(1 + \frac{0.05}{12}\right)^{12 \times 105} \] Calculating the components: 1. Calculate \( \frac{0.05}{12} \): \[ \frac{0.05}{12} \approx 0.00416667 \] 2. Calculate \( 12 \times 105 = 1260 \). 3. Calculate \( \left(1 + 0.00416667\right)^{1260} \): \[ \left(1.00416667\right)^{1260} \] Using a calculator for \( \left(1.00416667\right)^{1260} \): \[ \approx 5.127 \] 4. Finally, calculate the future value: \[ FV \approx 3,000,000 \times 5.127 \approx 15,381,000 \] Thus, the future value of the investment after 105 years at a 5% annual interest rate compounded monthly would be approximately **15,381,000**.