CHANGE IN INCOME –
Example.1) A man bought 360, $25 shares paying dividend at 12%, per annum. He sold them when price rose to $40 and invested the proceeds in $50 shares paying 10% dividend and quoted at $60. Find the change in his annual income.
Ans.) Income from shares of first kind –
Annual income from 1 share of first kind = 12% of $25
12
= $(25 X --------) = $3
100
Annual income from 360 shares of first kind = $(360 X 3) = $1080
Income from Shares of Second kind –
S.P. of 1 share of first kind = $40
S.P. of 360 shares of first kind = $(360 X 40) = $14400
Proceeds from shares of first kind = $14400
Market value of each share of second kind = $60
14400
Number of shares of second kind purchased = --------- = 240
60
Annual income from 1 share of second kind = 10% of $50
10
= $(50 X -------) = $5
100
Annual income from 240 shares of second kind = $(240 X 5) = $1200
Change in income = $(1200 – 1080) = $120 increased (Ans.)
Example.2) Sebastian invests $16500 partly in 10%, $100 shares at $130 and partly in 8%, $100 shares at $120. If her total annual income from these shares be $1180, find her investment in each kind of shares.
Ans.) Let the investment in first kind of shares be $a
Then, the investment in second kind of shares = $(16500 – a)
Income from 10%, $100 shares at $130.
By investing $130, income derived = $10
10 a
By investing $x, income derived = $(------- X a) = $ -------
130 13
Income from 8%, $100 shares at $120
By investing $120, income derived = $8
8
By investing $(16500 – a), income derived = $ [------- X (16500 – a)]
120
(16500 – a)
= $ -------------
15
But, total annual income derived from both kinds of shares = $1180
a (16500 – a)
So, -------- + -------------- = 1180
13 15
=> 15 a + 13 X (16500 – a) = (1180 X 13 X 15)
=> 2 a = (230100 – 214500) = 15600
=> a = 7800
Investment in 10%, $100 shares at $130 = $7800
Investment in 8%, $100 shares at $120 = $(16500 – 7800) = $8700 (Ans.)
Example.3) A man invested $29750 on 16%, $25 shares of a company. If he receives a dividend of $3400, find-
(i) the number of shares he bought
(ii) Market value of each share
Ans.) Suppose he purchased z shares
Face value of z shares = $25 z
Dividend = 16% of $25 z
16
= -------- X $25 z = $4 z
100
As per the condition –
$4 z = 3400
z = 850 ……………(i) (Ans.)
Total investment = $29750
Number of shares bought 850
29750
Market value of each shares = $ --------- = $35
850
Hence, the market value of each share is $35 …………….(ii) (Ans.)
Example.4) Robert invested $9600 on $100 shares at $20 premium paying 8% dividend. Robert sold the shares when the price rose to $160. He invested the proceeds (excluding dividend) in 10%, $50 shares at $40. Find the –
(i) Original number of shares
(ii) Sale proceeds
(iii) New number of shares
(iv) Change in the two dividends
Ans.) Amount invested $9600
Market value of each share = $120
9600
Original number of shares bought = -------- = 80 ………………….(i) (Ans.)
120
Market value of each share = $160
Number of shares = 80
Total sale value of these shares = $(160 X 80) = $12800
So, sale proceeds = $12800 ……………….(ii) (Ans.)
Market price of each share = $40
12800
New number of shares bought = --------- = 320 ………………(iii)
40
Face value of original 80 shares = $(80 X 100) = $8000
8
Dividend on it = 8% of $8000 = $(8000 X ------) = $640
100
Face value of new 320 shares = $(50 X 320) = $16000
Dividend on new shares = 10% of $16000
10
= $(16000 X -------) = $1600
100
Increase in dividend = $(1600 – 640) = $960 ………………………(iv) (Ans.)
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