A man buys a scooter on making a cash payment of ₹16,224 and promises to pay two more yearly instalment of equivalent amount in the next two years. If the rate of interest is 4% per annum compounded yearly, what is the cash value of the scooter?

Correct option is C

Given:
Cash paid now = ₹16,224
Two equal yearly instalments of ₹16,224 each
Rate of interest = 4% p.a. compounded yearly
Formula Used:

Cash value of the scooter = Present value of all payments
​$$\text{Present Value} = \frac{A}{(1 + r)^1} + \frac{A}{(1 + r)^2}$$​​
Where A = 16,224, r = 0.04
Solution:
​$$\text{PV of 1st instalment} = \frac{16,224}{1.04} =15,600$$

​$$\text{PV of 2nd instalment} = \frac{16,224}{(1.04)^2} = \frac{16,224}{1.0816} = 15,000$$

​$$\text{Total Cash Value} = 16,224 (\text{paid now}) + 15,600 + 15,000 = ₹46,824$$​​
Thus, the correct option is (c) ₹46,824

Alternate Method:

R = 4 % = $$+\frac{1}{25}$$​

So, Two equal yearly instalments = 
$$\frac{16224}{676} \times 1275$$ = 30600

Total Cash Value = 30600 + 16224 = ₹46,824​