An amount of R 2590 is invested in a savings account which pays a compound interest rate of \( 11,5 \% \) p.a. Calculate the balance accumulated by the end of 6 years. INSTRUCTION: As usual with financial calculations, round your answer to two decimal places, but do not round off until you have reached the solution.

To calculate the balance accumulated by the end of 6 years with compound interest, we can use the formula for compound interest: \[ A = P \times (1 + \frac{r}{100})^n \] Where: - \( A \) is the amount accumulated after \( n \) years, - \( P \) is the principal amount (initial investment), - \( r \) is the annual interest rate (in %), - \( n \) is the number of years. Given: - Principal amount (\( P \)) = R 2590, - Annual interest rate (\( r \)) = 11.5%, - Number of years (\( n \)) = 6. Substitute the given values into the formula: \[ A = 2590 \times (1 + \frac{11.5}{100})^6 \] Now, we can calculate the balance accumulated by the end of 6 years. Calculate the value by following steps: - step0: Calculate: \(2590\left(1+\frac{11.5}{100}\right)^{6}\) - step1: Divide the terms: \(2590\left(1+\frac{23}{200}\right)^{6}\) - step2: Add the numbers: \(2590\left(\frac{223}{200}\right)^{6}\) - step3: Simplify: \(2590\times \frac{223^{6}}{200^{6}}\) - step4: Rewrite the expression: \(10\times 259\times \frac{223^{6}}{200^{6}}\) - step5: Rewrite the expression: \(10\times 259\times \frac{223^{6}}{100^{6}\times 2^{6}}\) - step6: Rewrite the expression: \(10\times 259\times \frac{223^{6}}{10^{12}\times 2^{6}}\) - step7: Reduce the numbers: \(259\times \frac{223^{6}}{10^{11}\times 2^{6}}\) - step8: Multiply the fractions: \(\frac{259\times 223^{6}}{64\times 10^{11}}\) The balance accumulated by the end of 6 years is approximately R 4976.79.