N \( \$ 750 \) at \( 4 \% \) for 10 years

To calculate the future value of an investment, we can use the formula for compound interest: \[ FV = PV \times (1 + r)^n \] Where: - \( FV \) is the future value of the investment - \( PV \) is the present value of the investment (initial amount) - \( r \) is the annual interest rate (in decimal form) - \( n \) is the number of years the money is invested for Given: - Present value (PV) = $750 - Annual interest rate (r) = 4% = 0.04 - Number of years (n) = 10 Substitute the values into the formula: \[ FV = 750 \times (1 + 0.04)^{10} \] Now, we can calculate the future value of the investment. Calculate the value by following steps: - step0: Calculate: \(750\left(1+0.04\right)^{10}\) - step1: Add the numbers: \(750\times 1.04^{10}\) - step2: Convert the expressions: \(750\left(\frac{26}{25}\right)^{10}\) - step3: Simplify: \(750\times \frac{26^{10}}{25^{10}}\) - step4: Rewrite the expression: \(125\times 6\times \frac{26^{10}}{25^{10}}\) - step5: Rewrite the expression: \(5^{3}\times 6\times \frac{26^{10}}{5^{20}}\) - step6: Reduce the numbers: \(6\times \frac{26^{10}}{5^{17}}\) - step7: Multiply: \(\frac{6\times 26^{10}}{5^{17}}\) The future value of the investment of $750 at an annual interest rate of 4% for 10 years is approximately $1110.18.