Calculate the difference between the simple interest and the compound interest earned on $1 invested at 6% p.a. for 5 years.

To calculate the difference between the simple interest (SI) and the compound interest (CI) earned on $1 invested at 6% per annum for 5 years, we'll proceed with the following steps:

### 1. **Simple Interest (SI) Calculation**
The formula for simple interest is:
\[
\text{SI} = P \times r \times t
\]
Where:
- $ P $ is the principal amount = $1
- $ r $ is the annual interest rate = 6% = 0.06
- $ t $ is the time period = 5 years

\[
\text{SI} = 1 \times 0.06 \times 5 = 0.30 \text{ dollars}
\]

### 2. **Compound Interest (CI) Calculation**
The formula for compound interest is:
\[
\text{CI} = P \times \left(1 + \frac{r}{n}\right)^{nt} - P
\]
Where:
- $ P $ is the principal amount = $1
- $ r $ is the annual interest rate = 6% = 0.06
- $ t $ is the time period = 5 years
- $ n $ is the number of times interest is compounded per year = 1 (since it's compounded annually)

\[
\text{CI} = 1 \times \left(1 + \frac{0.06}{1}\right)^{1 \times 5} - 1 = 1 \times (1.06)^5 - 1
\]

Now, calculate $(1.06)^5$:

\[
(1.06)^5 \approx 1.3382
\]

Thus, the compound interest (CI) is:
\[
\text{CI} \approx 1.3382 - 1 = 0.3382 \text{ dollars}
\]

### 3. **Difference between CI and SI**
The difference between the compound interest and simple interest is:
\[
\text{Difference} = \text{CI} - \text{SI} = 0.3382 - 0.30 = 0.0382 \text{ dollars}
\]

### Final Answer:
The difference between the compound interest and the simple interest earned on $1 invested at 6% per annum for 5 years is approximately **$0.0382**.

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

Here are 8 related questions you might find useful:

1. What would the difference be if the interest were compounded semi-annually?
2. How would the result change if the interest rate were 8% instead of 6%?
3. What if the time period was only 3 years?
4. How do you calculate compound interest if compounded monthly?
5. What is the formula for compound interest when compounded continuously?
6. How does the difference between CI and SI change with increasing time?
7. Can you explain the significance of the interest rate in these calculations?
8. How does compound interest differ from simple interest conceptually?

**Tip:** Compound interest generally accumulates more over time compared to simple interest, especially as the number of compounding periods increases.

Learn how to calculate the difference between simple interest (SI) and compound interest (CI) on $1 invested at 6% per annum for 5 years. Detailed step-by-step solution with formulas and numerical calculations provided.

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