**Solve the following :**

A person purchases a television by paying ₹20,000 in cash and promising to pay ₹1,000 at end of every month for the next 2 years. If money is worth 12% p. a. converted monthly, find the cash price of the television. [(1.01)^{–24} = 0.7875]

#### Solution

Person buys the television for ₹20,000 in cash.

∴ First payment = ₹20,000

Remaining value of the television was paid in monthly instalments of ₹1,000.

∴ C= ₹1,000,

The duration of monthly installments is of 2 years.

∴ n = 24

Rate of interest is 12% p.a.

∴ r = `(12)/(12)` = 1% p.m.

∴ i = `"r"/(100) = (1)/(100)` = 0.01

The amount is paid at the end of every month.

∴ It is an immediate annuity.

Now, to find sum of all instalments we have to find present value.

∴ P = `"C"/"i"[1 - (1 + "i")^-"n"]`

∴ P = `(1,000)/(0.01)[1 - (1 + 0.01)^24]`

= 1,00,000 [1 – (1.01)^{–24}]

= 1,00,000 (1 – 0.7875)

= 1,00,000 x 0.2125

∴ P = ₹21,250

∴ Cash price of the television = First Payment + Present Value

= 20,000 + 21,250

= ₹41,250

∴ Cash price of the television is ₹41,250.