If for an immediate annuity `r = 10%` p.a., `P = 12,679.46` and `A = 18,564` then the amount of each annuity paid is______

Answer

To find the amount of each annuity paid, we can use the formula relating the present value (P), accumulated value (A), and the annuity payment (C) in an immediate annuity. Here are the steps:

### Step 1: Identify the given values
- Interest rate (r) = 10% per annum
- Present value (P) = 12,679.46
- Accumulated value (A) = 18,564

### Step 2: Convert the interest rate to decimal
The interest rate in decimal form is:
\[ I = \frac{r}{100} = \frac{10}{100} = 0.10 \]

### Step 3: Use the formula relating P, A, and C
We know the formula:
\[ \frac{1}{P} - \frac{1}{A} = \frac{I}{C} \]
Substituting the values we have:
\[ \frac{1}{12679.46} - \frac{1}{18564} = \frac{0.10}{C} \]

### Step 4: Calculate the left-hand side
Calculate \( \frac{1}{12679.46} \) and \( \frac{1}{18564} \):
\[ \frac{1}{12679.46} \approx 0.0000788 \]
\[ \frac{1}{18564} \approx 0.0000539 \]
Now, subtract these two values:
\[ 0.0000788 - 0.0000539 = 0.0000249 \]

### Step 5: Set up the equation
Now we have:
\[ 0.0000249 = \frac{0.10}{C} \]

### Step 6: Solve for C
Rearranging gives:
\[ C = \frac{0.10}{0.0000249} \]
Calculating this:
\[ C \approx 4016.06 \]

### Step 7: Round to the nearest whole number
Thus, the amount of each annuity paid is approximately:
\[ C \approx 4016 \]

### Final Answer
The amount of each annuity paid is **Rs. 4016**.

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