Calculate the difference between the simple interest and the compound interest earned on $1,200 invested at 1% p.a. for 5 years.

To find the difference between the simple interest and the compound interest earned on $1,200 invested at 1% per annum for 5 years, we will calculate each separately and then find the difference.

### 1. Simple Interest (SI)
The formula for simple interest is:

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

Where:
- $ P = 1200 $ (the principal amount)
- $ R = 1\% $ (annual interest rate)
- $ T = 5 $ years (time period)

\[
SI = \frac{1200 \times 1 \times 5}{100} = \frac{6000}{100} = 60
\]

So, the simple interest earned is $60.

### 2. Compound Interest (CI)
The formula for compound interest is:

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

Where:
- $ P = 1200 $
- $ R = 1\% $
- $ T = 5 $ years

\[
CI = 1200 \left(1 + \frac{1}{100}\right)^5 - 1200
\]

\[
CI = 1200 \left(1.01\right)^5 - 1200
\]

First, calculate $ 1.01^5 $:

\[
1.01^5 \approx 1.05101005
\]

Now, calculate the compound interest:

\[
CI = 1200 \times 1.05101005 - 1200 = 1261.21206 - 1200 = 61.21206
\]

So, the compound interest earned is approximately $61.21.

### 3. Difference Between Compound Interest and Simple Interest

\[
\text{Difference} = CI - SI = 61.21 - 60 = 1.21
\]

The difference between the compound interest and the simple interest is approximately **$1.21**.

Would you like more details or have any questions?

Here are 8 related questions you might find interesting:
1. How does the difference between simple and compound interest change with a higher interest rate?
2. What happens to the difference if the investment period is extended to 10 years?
3. How is compound interest affected by more frequent compounding periods, like semi-annually or quarterly?
4. What is the formula for continuous compounding, and how would it affect the investment?
5. How would the interest amounts change if the principal were doubled to $2,400?
6. Can you explain the difference in concepts between simple interest and compound interest?
7. How would the interest amounts differ if the rate were 2% instead of 1%?
8. What would be the impact on compound interest if the time period were reduced to 3 years?

**Tip:** Compound interest grows faster than simple interest because it calculates interest on both the initial principal and the accumulated interest from previous periods.

Learn how to calculate the difference between simple interest and compound interest on $1,200 invested at 1% per annum for 5 years. Detailed step-by-step solution with formulas and calculations provided.

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