Question

In 4 years, a mobile costing ₹36,000 will have a salvage value of ₹ 7200.

The following graph shows the depreciation of a mobile’s value over 4 years.

A new mobile at that time (i.e., after 4 years) is expected to cost for ₹ 55,200. In order to provide funds for the difference between the replacement cost and the salvage cost, a sinking fund is set up into which equal payments are placed at the end of each year. If the fund earns interest at the rate 7% compounded annually, how much should each payment be? Also find the amount of Annual Depreciation of the mobile’s value over 4 years and find the rate of depreciation (under straight line method). Use (1.07)⁴ = 1.3107.

Answer 1

Amount needed after 4 years 

= Replacement Cost - Salvage Cost

= ₹(55,200 - 7200)

= ₹48,000

The payments into sinking fund consisting of 10 annual payments at the rate 7% per year is given by

\(A=R S_{{n} \rceil i}=R\left[\frac{(1+i)^{n}-1}{i}\right]\)

\(\Rightarrow 48000=R\left[\frac{(1+0.07)^{4}-1}{0.07}\right]=R\left[\frac{(1.07)^{4}-1}{0.07}\right]\)

\(\Rightarrow R=\frac{48000}{4.4385}=₹ 10814.5\)

Amount of Annual Depreciation \(=\frac{36000-7200}{4}=\frac{28800}{4}=₹ 7200\)

and rate of Depreciation \(=\frac{7200}{36000-7200} \times 100=25 \%\)