A sum of Rs. 390200 is to paid back in three equal annual installments . How much is each instalment , if the rate of interest charged is 4% per annum compounded annually ?

Options

A. Rs. 140608
B. Rs. 120560
C. Rs 10000
D. Rs. 18000

Answer

To find the amount of each installment when a sum of Rs. 390,200 is to be paid back in three equal annual installments at an interest rate of 4% per annum compounded annually, we can use the formula for the present value of an annuity.

### Step-by-Step Solution:

1. **Identify the Variables**:
- Total amount (Present Value, PV) = Rs. 390,200
- Number of installments (n) = 3
- Rate of interest (r) = 4% per annum = 0.04

2. **Use the Present Value of Annuity Formula**:
The formula for the present value of an annuity is:
\[ PV = P \times \frac{1 - (1 + r)^{-n}}{r} \]
Where:
- \(PV\) = Present Value
- \(P\) = Amount of each installment
- \(r\) = Interest rate per period
- \(n\) = Number of periods

3. **Substitute the Known Values**:
\[ 390200 = P \times \frac{1 - (1 + 0.04)^{-3}}{0.04} \]

4. **Calculate the Annuity Factor**:
First, calculate \((1 + 0.04)^{-3}\):
\[ (1 + 0.04)^{-3} = (1.04)^{-3} \approx 0.889 \]
Now, substitute this back into the formula:
\[ 390200 = P \times \frac{1 - 0.889}{0.04} \]
\[ 390200 = P \times \frac{0.111}{0.04} \]
\[ 390200 = P \times 2.775 \]

5. **Solve for P**:
\[ P = \frac{390200}{2.775} \approx 140,000 \]

6. **Conclusion**:
Each installment is approximately Rs. 140,000.