Question

A sinking fund is created for the redemption of the debentures of Rs. 10000 at the end of 25 years. How much money should be provided out of profits each year for the sinking fund if the investment can earn interest at the rate 4% per annum?
(a) 2408.19
(b) 1408.19
(c) 3408.19
(d) 5408.19

Answer 1

Hint: First, before proceeding for this , we must know the following formula that is to be used to get the value of the sinking fund with time where r is rate of interest, A is the amount, n is the time in years and M is the debenture amount as $ M=\dfrac{A}{r}\left[ {{\left( 1+r \right)}^{n}}-1 \right] $ . Then, by substituting the value of the rate of interest as 4%, value of the debenture amount M as 10000 and value of the tenure in years n as 25 years, we can calculate the value of amount A, we get the desired value.

Complete step-by-step answer:
In this question, we are supposed to find the money provided out of profits each year for the sinking fund if the investment can earn interest at the rate 4% per annum for the redemption of debentures of Rs. 10,000 at the end of 25 years.
So, before proceeding for this , we must know the following formula that is to be used to get the value of the sinking fund with time where r is rate of interest, A is the amount, n is the time in years and M is the debenture amount.
Now, the formula for the sinking fund will be as:
 $ M=\dfrac{A}{r}\left[ {{\left( 1+r \right)}^{n}}-1 \right] $
Here, by substituting the value of the rate of interest as 4%, value of the debenture amount M as 10000 and value of the tenure in years n as 25 years, we can calculate the value of amount A.
So, by using all the above mentioned values, we get:
 $ 10000=\dfrac{A}{0.04}\left[ {{\left( 1+0.04 \right)}^{25}}-1 \right] $
Then, we can solve the above expression for the value of A as:
 $ \begin{align}
  & 400=A\left[ {{\left( 1.04 \right)}^{25}}-1 \right] \\
 & \Rightarrow 400=A\left[ 2.6658-1 \right] \\
 & \Rightarrow 400=1.6658A \\
 & \Rightarrow A=\dfrac{400}{1.6658} \\
 & \Rightarrow A=2408.19 \\
\end{align} $
So, the amount given out as a profit for the sinking fund is Rs. 2408.19.
So, the correct answer is “Option A”.

Note: Now, in this type of question, the only mistake we can make is to use the wrong formula for the future value of increasing funds confused with sinking funds. So, the formula for the two are as:
Formula for the sinking fund is $ M=\dfrac{A}{r}\left[ {{\left( 1+r \right)}^{n}}-1 \right] $
Formula for the increasing funds is $ F=\dfrac{{{\left( 1+r \right)}^{n}}-1}{r} $ .
So, we should be careful while using them as in this question, sinking funds is required.