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.

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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.
The balance accumulated by the end of 6 years is R 4976.79.

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