A washing machine is available at 18,000 cash or for 7,600 cash down payment flowed by two equalhalf yearly instalments of Rs. x each. If the rate of interest charged is 16% p.a. and conpounded half yearly,then what is the value of x?

Correct option is C

Given :

Cash price of washing machine = Rs. 18,000
Down payment = Rs. 7,600

Balance amount = 18,000 - 7,600 = 10,400

Rate of interest = 16% p.a. compounded half-yearly
Half-yearly rate = 8%

Number of instalments = 2 (half-yearly)

Formula Used :
Present Value of instalments = Cash price − Down payment

​$$\text{PV} = \frac{x}{(1+r)} + \frac{x}{(1+r)^2}$$​​
​Solution :​

Each instalment = Rs. x

here r = 8% = 0.08

10,400 =$$\frac{x}{1.08} + \frac{x}{(1.08)^2}$$​​

10,400 = $$x\left(\frac{1}{1.08} + \frac{1}{1.1664}\right)$$​​

10,400 = x(0.9259 + 0.8573)

10,400 = 1.7832x

x =$$\frac{10,400}{1.7832}$$​​

x$$\approx 5$$​,832