Calculate the future value of an annuity when regular annual payments of Rs 10,000 are made for 5 years, with an interest rate of 6% compounded annually. 



The future value (FV) of an annuity can be calculated using the formula:

\[
FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right)
\]

Where:
- \( P \) is the regular payment (Rs 10,000),
- \( r \) is the annual interest rate (6% or 0.06),
- \( n \) is the number of periods (5 years).

Let's calculate:

\[
FV = 10,000 \times \left( \frac{(1 + 0.06)^5 - 1}{0.06} \right)
\]

First, calculate \((1 + 0.06)^5\):

\[
(1.06)^5 = 1.338225
\]

Now, subtract 1:

\[
1.338225 - 1 = 0.338225
\]

Next, divide by the interest rate:

\[
\frac{0.338225}{0.06} = 5.637083
\]

Finally, multiply by the regular payment:

\[
FV = 10,000 \times 5.637083 = 56,370.83
\]

So, the future value of the annuity is **Rs 56,370.83**.

Would you like further details or have any questions?

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Here are 5 related questions for deeper understanding:
1. How does changing the interest rate affect the future value of the annuity?
2. What happens to the future value if the annuity period is extended to 10 years?
3. How would monthly compounding impact the future value?
4. What is the formula for the present value of an annuity, and how does it differ from future value?
5. How does the future value change if payments are made at the beginning of each period (annuity due)?

**Tip:** Always verify if the interest is compounded annually, monthly, or quarterly, as it significantly impacts the calculations!

Calculate the future value of an annuity when regular annual payments of Rs 10,000 are made for 5 years, with an interest rate of 6% compounded annually.

Learn how to calculate the future value of an annuity with Rs 10,000 annual payments for 5 years at a 6% interest rate, compounded annually. This example covers key financial concepts, including the future value formula and compound interest. Suitable for Grades 10-12.

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