Compound interest find the firal amount that 21200 will gron to invest for 5 tears at (1) \( 8 \% \) pa compoind interest? C2) 2,3 pa Compound interest

To find the final amount that $21200 will grow to after investing for 5 years at different compound interest rates, we can use the compound interest formula: \[ A = P \left( 1 + \frac{r}{100} \right)^n \] where: - \( A \) is the final amount - \( P \) is the principal amount (initial investment) - \( r \) is the annual interest rate - \( n \) is the number of years Let's calculate the final amount for each interest rate: 1. For 8% compound interest: \[ A = 21200 \left( 1 + \frac{8}{100} \right)^5 \] 2. For 2.3% compound interest: \[ A = 21200 \left( 1 + \frac{2.3}{100} \right)^5 \] Now, let's calculate the final amounts for each interest rate. Calculate the value by following steps: - step0: Calculate: \(21200\left(1+\frac{8}{100}\right)^{5}\) - step1: Reduce the fraction: \(21200\left(1+\frac{2}{25}\right)^{5}\) - step2: Add the numbers: \(21200\left(\frac{27}{25}\right)^{5}\) - step3: Simplify: \(21200\times \frac{27^{5}}{25^{5}}\) - step4: Rewrite the expression: \(25\times 848\times \frac{27^{5}}{25^{5}}\) - step5: Reduce the numbers: \(848\times \frac{27^{5}}{25^{4}}\) - step6: Multiply: \(\frac{848\times 27^{5}}{25^{4}}\) Calculate or simplify the expression \( 21200*(1+2.3/100)^5 \). Calculate the value by following steps: - step0: Calculate: \(21200\left(1+\frac{2.3}{100}\right)^{5}\) - step1: Divide the terms: \(21200\left(1+\frac{23}{1000}\right)^{5}\) - step2: Add the numbers: \(21200\left(\frac{1023}{1000}\right)^{5}\) - step3: Simplify: \(21200\times \frac{1023^{5}}{1000^{5}}\) - step4: Rewrite the expression: \(200\times 106\times \frac{1023^{5}}{1000^{5}}\) - step5: Rewrite the expression: \(200\times 106\times \frac{1023^{5}}{200^{5}\times 5^{5}}\) - step6: Reduce the numbers: \(106\times \frac{1023^{5}}{200^{4}\times 5^{5}}\) - step7: Rewrite the expression: \(2\times 53\times \frac{1023^{5}}{200^{4}\times 5^{5}}\) - step8: Rewrite the expression: \(2\times 53\times \frac{1023^{5}}{8^{4}\times 25^{4}\times 5^{5}}\) - step9: Rewrite the expression: \(2\times 53\times \frac{1023^{5}}{2^{12}\times 25^{4}\times 5^{5}}\) - step10: Reduce the numbers: \(53\times \frac{1023^{5}}{2^{11}\times 25^{4}\times 5^{5}}\) - step11: Multiply the fractions: \(\frac{53\times 1023^{5}}{6400000\times 25^{4}}\) The final amount that $21200 will grow to after investing for 5 years at 8% compound interest is approximately $31,149.76. The final amount that $21200 will grow to after investing for 5 years at 2.3% compound interest is approximately $23,752.76.