calculate the difference between simple and compound interest if R680 is invested at 8% p.a for 4 years

To calculate the difference between simple interest (SI) and compound interest (CI) for a principal amount \( P = 680 \) at an annual interest rate of \( R = 8\% \) over a period of \( T = 4 \) years, we need to compute both the simple interest and the compound interest first.

### Step 1: Calculate Simple Interest (SI)

The formula for simple interest is:

\[
SI = \frac{P \times R \times T}{100}
\]

Substitute the values:

\[
SI = \frac{680 \times 8 \times 4}{100}
\]

### Step 2: Calculate Compound Interest (CI)

The formula for compound interest, assuming interest is compounded annually, is:

\[
CI = P \left(1 + \frac{R}{100}\right)^T - P
\]

Substitute the values:

\[
CI = 680 \left(1 + \frac{8}{100}\right)^4 - 680
\]

### Step 3: Find the Difference Between CI and SI

The difference between compound interest and simple interest over the same period can be calculated as:

\[
\text{Difference} = CI - SI
\]

Let's compute these values.Here are the results:

1. **Simple Interest (SI):** R217.60
2. **Compound Interest (CI):** R245.13
3. **Difference between CI and SI:** R27.53

So, the compound interest is R27.53 more than the simple interest for the given investment over 4 years.

Would you like more details, or do you have any questions?

### Related Questions:
1. How would the difference change if the interest rate were 10%?
2. What would be the compound interest if it were compounded semi-annually?
3. How does the difference between CI and SI grow with an increase in the time period?
4. What is the effective annual rate (EAR) for an 8% compounded annually?
5. How to calculate compound interest if interest is compounded quarterly?

#### Tip:
The difference between compound and simple interest increases as the compounding frequency or time period increases.

Learn how to calculate the difference between simple interest (SI) and compound interest (CI) for an investment of R680 at 8% per annum over 4 years. Includes step-by-step calculations and results: SI = R217.60, CI = R245.13, Difference = R27.53.

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