Question

A machine cost Rs.60,000 and its effective life is estimated to be 25 years. A sinking fund is created for replacing the machine at the end of its lifetime when its scrap value is estimated Rs.5,000. The price of the new machine is estimated to be 100% more than the price of the present one. Find the amount that should be set aside at the end of each year, out of the profits, for the sinking fund if it accumulates at an interest 6% per annum compounded annually.

Answer 1

Hint: Compound interest is calculated based on the initial principal amount and the accumulated interest of previous periods. The formula for compound amount is given by \[A=P{{\left( 1+\dfrac{r}{100} \right)}^{t}}\]. This is the formula applicable for calculation of compound amount when it is compounded annually or per annum

Complete step-by-step answer:
Given the machine cost=60,000
A sinking fund is created so that the scrap value =5,000
Given that the price of new machine is 100% more than that of present one
So, amount needed for buying new machine =\[2\times 60,000=1,20,000\]
So, the effective amount needed for buying new machine = total amount needed – scrap value
                                                                                                       = \[1,20,000-5,000\]
                                                                                                        =\[1,15,000\]
The rate of interest per annum=6%
We know that the formula corresponding to these is given by \[A=P{{\left( 1+\dfrac{r}{100} \right)}^{t}}\]. . . . . . . . . . . . . . . .(1)
Substituting the corresponding values in the formula we will get,
\[\Rightarrow 12,000=P{{\left( 1+\dfrac{6}{100} \right)}^{25}}\]
\[\Rightarrow 12,000=P{{\left( 1+0.06 \right)}^{25}}\]
\[\Rightarrow P=\dfrac{12,000}{{{\left( 1.06 \right)}^{25}}}=\dfrac{12,000}{4.291}=27965\]
So, the amount that must be set aside at the end of year, out of profits is \[27965\]

Note: The above formula \[A=CI+P\] will give us the total amount.
A=amount
CI=compound interest
P=principal amount.
To calculate the compound interest we need to subtract the principal from the amount. Note that simple interest and compound interest are different.