CLASS-10CHANGE IN INCOME

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.)