ind the present value of an ordinary annuity of 8 quarterly payments of ₹500 each, the 
rate of interest being 8% p.a. compound quarterly

To find the present value of an ordinary annuity with the given parameters, we use the formula for the present value of an ordinary annuity:

\[ PV = \frac{PMT \times (1 - (1 + r)^{-n})}{r} \]

where:
- \( PV \) is the present value of the annuity.
- \( PMT \) is the payment amount per period.
- \( r \) is the periodic interest rate.
- \( n \) is the total number of payments.

Given:
- Quarterly payments (\( PMT \)) = ₹500
- Annual interest rate = 8% per annum compounded quarterly
- Number of payments (\( n \)) = 8 quarters

First, we need to convert the annual interest rate to a quarterly interest rate:

\[ r = \frac{8\%}{4} = 2\% = 0.02 \]

Now, we can plug these values into the formula:

\[ PV = \frac{500 \times (1 - (1 + 0.02)^{-8})}{0.02} \]

Let's compute this step by step:

1. Calculate \( (1 + 0.02)^{-8} \):
   \[ (1 + 0.02)^{-8} = (1.02)^{-8} \approx 0.8512 \]

2. Subtract this value from 1:
   \[ 1 - 0.8512 = 0.1488 \]

3. Multiply by the payment amount and divide by the periodic interest rate:
   \[ PV = \frac{500 \times 0.1488}{0.02} = \frac{74.4}{0.02} = 3720 \]

So, the present value of the ordinary annuity is ₹3,720.

Would you like further details or have any questions?

Here are 5 related questions that you might find helpful:
1. How would the present value change if the interest rate were different?
2. What is the future value of this annuity after the last payment is made?
3. How do you calculate the present value of an annuity due?
4. What is the effect of increasing the number of payments on the present value?
5. How would the calculation change if the payments were made annually instead of quarterly?

**Tip:** When dealing with annuities, always ensure that the interest rate and the number of periods are consistent with the payment frequency (e.g., quarterly, annually).

Find the present value of an ordinary annuity of 8 quarterly payments of ₹500 each, the rate of interest being 8% p.a. compounded quarterly.

Learn how to calculate the present value of an ordinary annuity of ₹500 paid quarterly for 8 periods, with an 8% annual interest rate compounded quarterly. This solution provides a step-by-step explanation using the present value formula, relevant to students in Grades 10-12.

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