Rakesh bought a scooter on the condition that the would pay ₹ 12,000 instantly and ₹ 1,680 after one year and ₹ 5,292 after two years. If the payment is at 5% compound interest, then what was the cost price of scooter.

Options

A. ₹ 18,400
B. ₹ 18,000
C. ₹20,000
D. ₹21,400

Answer

To find the cost price of the scooter Rakesh bought, we need to calculate the present value of all the payments he made, considering the compound interest rate of 5%.

### Step-by-Step Solution:

1. **Identify the Payments**:
- Rakesh pays ₹12,000 instantly.
- He pays ₹1,680 after one year.
- He pays ₹5,292 after two years.

2. **Calculate Present Value of Future Payments**:
- The present value (PV) formula for a future payment is given by:
\[ PV = \frac{FV}{(1 + r)^n} \]
where:
- \(FV\) = Future Value (the payment made in the future)
- \(r\) = interest rate (5% or 0.05)
- \(n\) = number of years until payment

3. **Calculate Present Value of ₹1,680 (after 1 year)**:
\[ PV_1 = \frac{1680}{(1 + 0.05)^1} = \frac{1680}{1.05} = 1600 \]

4. **Calculate Present Value of ₹5,292 (after 2 years)**:
\[ PV_2 = \frac{5292}{(1 + 0.05)^2} = \frac{5292}{1.1025} \approx 4800 \]

5. **Total Present Value of Payments**:
- Now, sum up all the present values:
\[ \text{Total PV} = 12000 + PV_1 + PV_2 = 12000 + 1600 + 4800 \]
\[ \text{Total PV} = 12000 + 1600 + 4800 = 18400 \]

6. **Conclusion**:
- Therefore, the cost price of the scooter is ₹18,400.