\( \$ 38,500 \) at \( 2 \% \) for 4 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) = $38,500 - Annual interest rate (r) = 2% = 0.02 - Number of years (n) = 4 years Substitute the given values into the formula: \[ FV = 38,500 \times (1 + 0.02)^4 \] Now, we can calculate the future value of the investment. Calculate the value by following steps: - step0: Calculate: \(38500\left(1+0.02\right)^{4}\) - step1: Add the numbers: \(38500\times 1.02^{4}\) - step2: Convert the expressions: \(38500\left(\frac{51}{50}\right)^{4}\) - step3: Simplify: \(38500\times \frac{51^{4}}{50^{4}}\) - step4: Rewrite the expression: \(50\times 770\times \frac{51^{4}}{50^{4}}\) - step5: Reduce the numbers: \(770\times \frac{51^{4}}{50^{3}}\) - step6: Rewrite the expression: \(10\times 77\times \frac{51^{4}}{50^{3}}\) - step7: Rewrite the expression: \(10\times 77\times \frac{51^{4}}{10^{3}\times 5^{3}}\) - step8: Reduce the numbers: \(77\times \frac{51^{4}}{10^{2}\times 5^{3}}\) - step9: Multiply: \(\frac{77\times 51^{4}}{12500}\) The future value of the investment of $38,500 at an annual interest rate of 2% for 4 years is approximately $41,673.64.