Find the balance after 8 years if \( \$ 37400 \) is invested at \( 7 \% \) p.a. compounded annually.

To find the balance after 8 years when $37400 is invested at 7% p.a. compounded annually, we can use the formula for compound interest: \[ A = P \left( 1 + \frac{r}{100} \right)^n \] where: - \( A \) is the amount after \( n \) years, - \( P \) is the principal amount (initial investment), - \( r \) is the annual interest rate (in %), - \( n \) is the number of years. Given: - \( P = \$37400 \), - \( r = 7\% \), - \( n = 8 \) years. Substitute these values into the formula to find the balance after 8 years. Calculate the value by following steps: - step0: Calculate: \(37400\left(1+\frac{7}{100}\right)^{8}\) - step1: Add the numbers: \(37400\left(\frac{107}{100}\right)^{8}\) - step2: Simplify: \(37400\times \frac{107^{8}}{100^{8}}\) - step3: Rewrite the expression: \(100\times 374\times \frac{107^{8}}{100^{8}}\) - step4: Reduce the numbers: \(374\times \frac{107^{8}}{100^{7}}\) - step5: Rewrite the expression: \(2\times 187\times \frac{107^{8}}{100^{7}}\) - step6: Rewrite the expression: \(2\times 187\times \frac{107^{8}}{4^{7}\times 25^{7}}\) - step7: Rewrite the expression: \(2\times 187\times \frac{107^{8}}{2^{14}\times 25^{7}}\) - step8: Reduce the numbers: \(187\times \frac{107^{8}}{2^{13}\times 25^{7}}\) - step9: Multiply the fractions: \(\frac{187\times 107^{8}}{8192\times 25^{7}}\) The balance after 8 years when $37400 is invested at 7% p.a. compounded annually is approximately $64260.16.