Question

Amit Kumar invests Rs. 36,000 in buying Rs 100 shares at Rs. 20 premium. The dividend is 15% per annum. Find:
(i)The number of shares he buys
(ii)His yearly dividend
(iii)The percentage return on his investment.
Give your Answer correct to the nearest whole number.

Answer 1

Hint: In this question we are given with the investment, face value or buying shares, premium, dividend or we can say discount. From these values we can calculate the number of shares i.e \[\dfrac{{investment}}{{market\,{\rm{ }}value}}\] and market value can be calculated by adding face value and premium. Then we can calculate dividend by calculating number of shares and percentage return on his investment will be calculated by \[\dfrac{{yearly\,{\rm{ dividend}}}}{{investment}} * 100\] .

Formula Used:
 \[no\,{\rm{ of\, shares = }}\dfrac{{investment}}{{market{\rm{ }}value}}\] , \[market\,{\rm{ value = face\, value + Premium}}\]\[Yearly\,{\rm{ Dividend = Percentage\, of\, dividend}} * {\rm{(face value}} * {\rm{no\, of\, shares)}}\]\[Percentage\,{\rm{ }}return\,{\rm{ on\, his\, investment}} = \dfrac{{yearly\,{\rm{ dividend}}}}{{investment}} * 100\]

Complete step-by-step answer:
 As, it is given investment=Rs.36000, Face value=Rs.100, Premium=Rs.20,
Dividend=15% per annum.
Here, firstly we will calculate \[market\,{\rm{ value = face\, value + Premium}}\]
\[\therefore {\rm{market value = 100 + 20}}\]
\[ \Rightarrow market{\rm{ value = 100Rs}}{\rm{.}}\]
Now, we will calculate (i) The number of shares he buys: \[no\,{\rm{ of\, shares\, = }}\dfrac{{investment}}{{market{\rm{ }}value}}\]
As, we have both investment and market value.
Now, we can calculate no. of shares \[{\rm{ = }}\dfrac{{36000}}{{120}}\]
Let’s divide by 120 to both numerator and denominator.
\[no\,{\rm{ of\, shares = 300Rs}}{\rm{.}}\]
(ii)His yearly Dividend: \[Yearly\,{\rm{ Dividend = Percentage\, of\, dividend}} * {\rm{(face\, value}} * {\rm{no\, of\, shares)}}\]
As we have Percentage of dividend , face value as well as no of shares.
So, we can calculate now Yearly Dividend \[ = 15\% {\rm{ }}\,of\,{\rm{ }}(100 * 300)\]
Yearly Dividend \[ = \dfrac{{15}}{{100}}(100 * 300)\]
Cancelling out zeros with each other.
We get, Yearly Dividend \[{\rm{ = 15}} * 300\] .
Yearly Dividend \[{\rm{ = 4500Rs}}{\rm{.}}\]
(iii) The percentage return on his investment:
Percentage return on his investment \[ = \dfrac{{yearly\,{\rm{ }}\,dividend}}{{investment}} * 100\]
We have calculated both yearly dividend and investment and hence putting the values in the formula.
Percentage return on his investment \[ = \dfrac{{4500}}{{36000}} * 100\]
Cancelling out zeros with each other.
Percentage return on his investment \[ = \dfrac{{450}}{{36}}\]
Let’s divide by 9 to both numerator and denominator.
We get,
Percentage return on his investment \[ = \dfrac{{50}}{4}\]
Now, divide 50 by 4.
Percentage return on his investment \[ = 12.5\% \]
Here, we have to give an answer in the nearest whole number.
So, we get Percentage return on his investment \[ = 13\% \] .

Note: We can calculate these questions by learning these formulas and implementing these values in a correct manner and calculating it very precisely. For rounding it to the nearest whole number we can check if the value in points is greater or equal than 5 then its higher number then rounding or if it’s less than 5, then we will round it off to original value.