Find the amount of an ordinary annuity if a payment of Rs. 500 is made at the end of every quarter for 5 years at the rate of 12% per annum compounded quarterly.

Answer

To find the amount of an ordinary annuity given a payment of Rs. 500 made at the end of every quarter for 5 years at an interest rate of 12% per annum compounded quarterly, we can follow these steps:

### Step 1: Identify the parameters
- Payment per period (C) = Rs. 500
- Annual interest rate (R) = 12%
- Compounding frequency (n) = quarterly = 4 times a year
- Total number of years (t) = 5 years

### Step 2: Calculate the effective interest rate per period
The effective interest rate per quarter (i) can be calculated as:
\[ i = \frac{R}{n} = \frac{12\%}{4} = 3\% = \frac{3}{100} = 0.03 \]

### Step 3: Calculate the total number of periods
The total number of periods (N) is given by:
\[ N = n \times t = 4 \times 5 = 20 \text{ quarters} \]

### Step 4: Use the annuity formula
The formula for the future value of an ordinary annuity is:
\[ A = C \times \frac{(1 + i)^N - 1}{i} \]
Substituting the values we have:
\[ A = 500 \times \frac{(1 + 0.03)^{20} - 1}{0.03} \]

### Step 5: Calculate \((1 + i)^N\)
First, calculate \((1 + 0.03)^{20}\):
\[ (1 + 0.03)^{20} = (1.03)^{20} \]
Using a calculator, we find:
\[ (1.03)^{20} \approx 1.8061 \]

### Step 6: Substitute back into the annuity formula
Now substitute this value back into the formula:
\[ A = 500 \times \frac{1.8061 - 1}{0.03} \]
\[ A = 500 \times \frac{0.8061}{0.03} \]
\[ A = 500 \times 26.87 \approx 13435 \]

### Final Answer
The amount of the ordinary annuity is approximately Rs. 13,435.

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