\begin{tabular}{l} Gielie invests R12 500 for 3 years at $$ 8,25 \% $$ compound interest. How much interest \ did he earn after 3 years? \ \hline\end{tabular}

Question

UpStudy AI · Accepted Answer

To find the interest earned by Gielie after 3 years, we can use the formula for compound interest:

$$ A = P(1 + \frac{r}{100})^n $$

where:
- $$ A $$ is the amount after $$ n $$ years,
- $$ P $$ is the principal amount (initial investment),
- $$ r $$ is the annual interest rate,
- $$ n $$ is the number of years.

Given:
- Principal amount ($$ P $$) = R12 500,
- Annual interest rate ($$ r $$) = 8.25%,
- Number of years ($$ n $$) = 3 years.

We need to calculate the interest earned after 3 years. The interest earned is the difference between the amount after 3 years and the principal amount.

Let's calculate the amount after 3 years using the compound interest formula and then find the interest earned.
Calculate the value by following steps:
- step0: Calculate:
  $$12500\left(1+\frac{8.25}{100}\right)^{3}$$
- step1: Divide the terms:
  $$12500\left(1+\frac{33}{400}\right)^{3}$$
- step2: Add the numbers:
  $$12500\left(\frac{433}{400}\right)^{3}$$
- step3: Simplify:
  $$12500\times \frac{433^{3}}{400^{3}}$$
- step4: Rewrite the expression:
  $$100\times 125\times \frac{433^{3}}{400^{3}}$$
- step5: Rewrite the expression:
  $$100\times 125\times \frac{433^{3}}{100^{3}\times 4^{3}}$$
- step6: Reduce the numbers:
  $$125\times \frac{433^{3}}{100^{2}\times 4^{3}}$$
- step7: Rewrite the expression:
  $$125\times \frac{433^{3}}{25^{2}\times 4^{2}\times 4^{3}}$$
- step8: Rewrite the expression:
  $$5^{3}\times \frac{433^{3}}{5^{4}\times 4^{2}\times 4^{3}}$$
- step9: Reduce the numbers:
  $$1\times \frac{433^{3}}{5\times 4^{2}\times 4^{3}}$$
- step10: Multiply:
  $$\frac{433^{3}}{5120}$$
The amount after 3 years is approximately R15,856.00332.

To find the interest earned, we subtract the principal amount from the amount after 3 years:

Interest earned = Amount after 3 years - Principal amount
Interest earned = R15,856.00332 - R12,500
Interest earned = R3,356.00332

Therefore, Gielie earned R3,356.00332 in interest after 3 years.
Gielie earned approximately R3,356 in interest after 3 years.

\begin{tabular}{l} Gielie invests R12 500 for 3 years at \( 8,25 \% \) compound interest. How much interest \\ did he earn after 3 years? \\ \hline\end{tabular}

Solución de inteligencia artificial de Upstudy

Responder

Solución

Mind Expander

preguntas relacionadas

Latest Arithmetic Questions