Calculate the difference between the simple interest and the compound interest earned on $3000 invested at 6% p.a. for 5 years.




To calculate the difference between the simple interest and the compound interest earned on $3,000 invested at 6% per annum for 5 years, follow these steps:

### Step 1: Calculate the Simple Interest (SI)
The formula for simple interest is:
\[
\text{Simple Interest (SI)} = P \times r \times t
\]
Where:
- $ P = 3000 $ (principal amount)
- $ r = \frac{6}{100} = 0.06 $ (annual interest rate)
- $ t = 5 $ (time in years)

\[
\text{SI} = 3000 \times 0.06 \times 5 = 900
\]

### Step 2: Calculate the Compound Interest (CI)
The formula for compound interest is:
\[
\text{Compound Interest (CI)} = P \times \left(1 + \frac{r}{n}\right)^{nt} - P
\]
Where:
- $ n = 1 $ (compounded annually, so $ n = 1 $)
- All other variables are as previously defined.

\[
\text{CI} = 3000 \times \left(1 + 0.06\right)^{5} - 3000
\]
\[
\text{CI} = 3000 \times \left(1.06\right)^{5} - 3000
\]
\[
\left(1.06\right)^{5} \approx 1.338225
\]
\[
\text{CI} = 3000 \times 1.338225 - 3000
\]
\[
\text{CI} = 4014.675 - 3000 = 1014.675
\]

### Step 3: Calculate the Difference Between CI and SI
\[
\text{Difference} = \text{CI} - \text{SI} = 1014.675 - 900 = 114.675
\]

So, the difference between the compound interest and simple interest is **$114.68** (rounded to two decimal places).

Would you like more details or have any questions?

Here are some related questions you might find interesting:
1. What will be the compound interest if the interest is compounded semi-annually?
2. How much more interest would you earn if the rate was 7% instead of 6% for the same period?
3. What would be the difference in interest if the investment period was 10 years instead of 5?
4. How does the difference between CI and SI change if the principal amount is doubled?
5. What is the total amount after 5 years for both simple interest and compound interest?

**Tip:** Compound interest grows faster than simple interest because it adds the interest to the principal before calculating the interest for the next period.

Learn how to calculate the difference between simple interest and compound interest earned on $3,000 invested at 6% per annum for 5 years. Includes step-by-step calculation using formulas for simple interest and compound interest. Suitable for high school students learning about interest calculations.

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