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To solve this compound interest problem, we will use the formula for compound interest:

\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
Where:
- $ A $ is the amount of money accumulated after $ t $ years, including interest.
- $ P $ is the principal amount ($10,000).
- $ r $ is the annual interest rate (3%, or 0.03 as a decimal).
- $ n $ is the number of times interest is compounded per year (annually $ n = 1 $ or monthly $ n = 12 $).
- $ t $ is the time in years (5 years).

The compound interest (CI) can be calculated as:
\[
CI = A - P
\]

Let's calculate the compound interest in both cases (a) annually and (b) monthly. I'll do the calculations.The compound interest for each case is:

(a) **Annually compounded**: $ CI = \$1592.74 $

(b) **Monthly compounded**: $ CI = \$1616.17 $

Would you like more details on the steps or any further clarification?

Here are some related questions you might want to explore:
1. How does the frequency of compounding affect compound interest?
2. What is the formula for continuous compounding?
3. How does increasing the principal affect the final interest?
4. How can we calculate the interest if the rate is compounded quarterly?
5. What is the difference between simple interest and compound interest?

**Tip**: Compounding more frequently increases the total interest accrued over time.

Find the compound interest on $10000 for 5 years at 3% per annum, compounded (a) Annually (b) Monthly.

Learn how to calculate compound interest for a principal of $10000 over 5 years at an interest rate of 3%, compounded annually and monthly. Explore key formulas and step-by-step solutions for both scenarios, suitable for students in Grades 10-12.

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