Calculation of Annuity Amount

Given:
- Time period (n) = 25 years
- Rate of interest (r) = 5% per annum (p.a.)
- Compound Interest (C.I.) = Rs. 50,000

To find:
- Annuity amount

Step 1: Calculate the Future Value
The future value (FV) of an annuity can be calculated using the formula:

FV = P * [(1 + r)^n - 1] / r

Where:
- P is the annuity payment (to be determined)
- r is the rate of interest per period (5% p.a.)
- n is the number of periods (25 years)

Substituting the given values, we have:

FV = P * [(1 + 0.05)^25 - 1] / 0.05

Step 2: Solve for Annuity Amount
Given that the compound interest (C.I.) after 25 years is Rs. 50,000, we can write the equation:

FV = P * [(1 + r)^n - 1] / r = Rs. 50,000

Now, we need to solve this equation to find the annuity amount (P).

Step 3: Simplify the Equation
Let's simplify the equation to solve for P:

P * [(1 + 0.05)^25 - 1] / 0.05 = Rs. 50,000

[(1.05)^25 - 1] / 0.05 = 50,000 / P

[(1.05)^25 - 1] = (50,000 / P) * 0.05

[(1.05)^25 - 1] = 2,500 / P

Step 4: Solve for P
To solve for P, we rearrange the equation:

P = 2,500 / [(1.05)^25 - 1]

Using a calculator or spreadsheet, we can evaluate the right-hand side of the equation:

P ≈ 2,500 / (1.80194 - 1)

P ≈ 2,500 / 0.80194

P ≈ 3,116.63

Therefore, the annuity amount is approximately Rs. 3,116.63.