Subash purchased a refrigerator on the terms that he is required to pay 1,500 cash down payment followed by 1,020 at the end of first year, 1,003 at the end of second year and 990 at the end of third year. Interest is charged at the rate of 10% per annum. Calculate the cash price:

Options

A. 3000
B. 2000
C. 4000
D. 5000

Answer

To calculate the cash price of the refrigerator that Subash purchased, we need to find the present value of all future payments, including the down payment. The interest rate is given as 10% per annum.

### Step-by-Step Solution:

1. **Identify the Payments**:
- Down payment: \( P_0 = 1500 \)
- Payment at the end of the first year: \( P_1 = 1020 \)
- Payment at the end of the second year: \( P_2 = 1003 \)
- Payment at the end of the third year: \( P_3 = 990 \)

2. **Calculate Present Value of Future Payments**:
The present value (PV) of each future payment can be calculated using the formula:
\[ PV = \frac{F}{(1 + r)^n} \]
where:
- \( F \) is the future payment,
- \( r \) is the interest rate (10% or 0.10),
- \( n \) is the number of years until the payment is made.

- **For the first year payment**:
\[ PV_1 = \frac{1020}{(1 + 0.10)^1} = \frac{1020}{1.10} \approx 927.27 \]

- **For the second year payment**:
\[ PV_2 = \frac{1003}{(1 + 0.10)^2} = \frac{1003}{1.21} \approx 828.10 \]

- **For the third year payment**:
\[ PV_3 = \frac{990}{(1 + 0.10)^3} = \frac{990}{1.331} \approx 743.49 \]

3. **Sum the Present Values**:
Now, we will sum the present values of all payments including the down payment:
\[ \text{Total Cash Price} = P_0 + PV_1 + PV_2 + PV_3 \]
\[ \text{Total Cash Price} = 1500 + 927.27 + 828.10 + 743.49 \]
\[ \text{Total Cash Price} \approx 1500 + 927.27 + 828.10 + 743.49 \approx 3998.86 \]

4. **Final Result**:
The cash price of the refrigerator is approximately **3998.86**.