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, - Mathematics and Statistics

Sum

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.

Concept: Annuity
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Balbharati Mathematics and Statistics 2 (Commerce) 12th Standard HSC Maharashtra State Board
Chapter 2 Insurance and Annuity
Miscellaneous Exercise 2 | Q 4.18 | Page 31