A cycle is being sold for Rs.500 upfront payment and after one month for Rs.610 instalment. If interest is being charged at 20% p.a. then find the cash price of the cycle.

Correct option is A

1. Given:

- Upfront payment: Rs. 500

- Instalment after one month: Rs. 610

- Interest rate: 20% p.a.

2. Formula Used:

- Present Value (PV) = $$\frac{\text{Future Value}}{1 + \text{Interest Rate per Month}}$$​

- Monthly Interest Rate = $$\frac{\text{Annual Interest Rate}}{12}$$​

3. Solution:

Monthly interest rate:

​$$\frac{20}{12} = \frac{5}{3}\% = 0.01667$$​

Present value of the instalment after one month:

​$$\text{PV of Rs. 610} = \frac{610}{1 + 0.01667} = \frac{610}{1.01667} \approx 600$$​

Total cash price:

Cash Price = 500 + 600 = 1100

Therefore, the correct option is **A. Rs. 1100 **.