a = Rs.1500; i = 12/100 = 0.12
P = \(\frac { a }{ i } =\frac { 1500 }{ 0.12 } \) = Rs.12,500
The person has to deposit Rs.12,500 to meet this expense.

Let the number of shares be x.
Dividend = No.of shares x F.V x Rate percentage.
1620 =  \(x \times 20 \times \frac { 9 }{ 100 } \)
x = \(\frac { 1620\times 100 }{ 20\times 9 } \) = 900 shares

Face value = Rs. 100
Market value = Rs. (100 – 17 + 1) = Rs. 84
\(\therefore\) percentage of his income = \(\frac{(12\times 100)}{84}\)
= \(\frac{100}{7}=14\frac{2}{7}\)
\(\therefore\) % of Income = \(14\frac{2}{7}\%\)

Number of shares = 500
Face value of a share = Rs. 100
Discount = Rs. 14
Market value of a share = 100 – 14 = Rs. 86 (face value – discount)
Market value of 500 shares = Number of shares × market value of a share
= 500 × 86 = 43,000
Market value of 500 shares = Rs. 43,000

a = Rs. 900, i = \(\cfrac { 8 }{ 200 } \) = 0.04, n = 6 x 2 = 12
P = \(\cfrac { a }{ i } \left[ 1-\left( 1+i \right) ^{ -n } \right] \)
\(=\cfrac { 900 }{ 0.04 } \left[ 1-\left( 1.04 \right) ^{ -12 } \right] \)
= 22500 [1 - 0.6252] 
= Rs. 8433

a = Rs. 2000, i = \(\cfrac { 8 }{ 400 } \) = 0.02, n = 10 x 4 = 40
\(A=\cfrac { a }{ i } \left[ \left( 1+i \right) ^{ n }-1 \right] \)
= \(\cfrac { 2000 }{ 0.02 } \left[ \left( 1.02 \right) ^{ 40 }-1 \right] \)
= 1,00,000 [2.2080-1]
= 100,000 [1.2080]
= Rs.1,20,800

Here A = 20,00,000 ; i = \(\frac{10}{100}=0.1\) n = 20 and k = 12
\(A=\frac{a}{i/k}[1+\frac{i}{k}^{nk}-1]\)
\(20,00,000=\frac{\frac{a}{0.1}}{12}[(1+\frac{0.1}{12})^{20\times 12}-1]\)
\(=\frac{12a}{0.1}[(1+\frac{0.1}{12})^{240}-1]\)
\(=12a[(\frac{12.1}{12})^{240}-1]\)
= 120a [(1.0083)²⁴⁰–1]
= 120a [6.194–1]
= 120a (5.194)
⇒ a = \(\frac{20,00,000}{120\times 2.194}\) = 3208.83
∴ a ≈ 3,209
Rs. 3,209 is to be deposited at the end of every month.

a = Rs. 2000, i = \(\frac{10}{100}\) = 0.1 n = 14
P = \(\cfrac { a }{ i } \left[ 1-\left( 1+i \right) ^{ -n } \right] \)
\(=\cfrac { 2000 }{ 0.1 } \left[ 1-\left( 1.1 \right) ^{ -14 } \right] \)
= 20000[1-0.2632]   
= Rs. 14,736

Number of preferential shares = 50,000
Number of ordinary shares = 2500
Total dividend = Total profit - Amount kept in reserve - Depreciation amount
= 1,60,000 - 20,000 - 10,000 = 1,30,000
Income from preferential shares
\(=50,000 \times 10 \times \frac{16}{100} \)
= 80,000
\(\therefore\) Income from ordinary shares
=1,30,000 - 80,000 = 50,000
Let x % be the rate of dividend for ordinary shares
\(50,000 =2500 \times 10 \times \frac{x}{100} \)
\(x =\frac{50,000}{250}=20 \%\)

Shares of tea company
No.of shares = 2000
FV = Rs.10
MV = Rs.33
Rate of dividend = 25%
S.P of a share = Rs.33
S.P of 2000 shares = 2000 x 33 = Rs. 66,000
Shares of cotton textiles
Investment = Rs. 66,000
FV = Rs. 25
MV = Rs. 44
Dividend =15%
(i) Number of cotton textile shares
= \(\frac {\text{ Investment} }{ M.V } \)
=  \(\frac { 66,000 }{ 44 } =1500\)
(ii) Income from tea company shares
= 2000 x 10 x \(\frac { 25 }{ 100 } \) = Rs. 5000
Income from cotton textiles shares
= 1 500 x 25 x \(\frac { 15 }{ 100 } \) = Rs. 5625
Change in his dividend income = 5625 - 5000 = Rs. 625

Machine A:
Present value of out flow = Rs.15,000
a = Rs. 4000, i = 8/100 = 0.08, n = 4
P = \(\cfrac { a }{ i } =\left[ 1-\left( 1+i \right) ^{ -n } \right] \)
\(=\frac{4000}{0.08}\left[1-\frac{1}{(1.08)^4}\right]\)
= 50000 [1 -(1.08)^-4]
= 50000 [1 -0.7350] = Rs.13240
Present inflow is less then present outflow 
Net outflow = 15,000 - 13,250 = Rs.1750.
Machine B
a = 7000, i = 0.08, n = 7
P = \(\cfrac { a }{ i } \left[ 1-\left( 1+i \right) ^{ -n } \right] \)
= \(\cfrac { 7000 }{ 0.08 } \left[ 1-\left( 1.08 \right) ^{ -7 } \right] \)
= 87500(1-0.05835)
= 87500 x 0.4165 = Rs.36,443.75
Present inflow is more than present outflow.
Net inflow = 36,443.75 - 20000
= Rs. 16,443.75
Machine Ycan be purchased.

Market value of one share
= 10 + 2.50 = Rs. 12.50
(i) Number of share =\(\frac {\text { Investment }}{ \text {Market \ Value } }\)
400 = \(\frac { \text {Investment} }{ 12.50 } \)
Investment = 400 x 12.50 = Rs. 5000
(ii) Annual dividend = Number of shares x F.V x Rate of dividend
= 400 x10 x \(\frac { 12 }{ 100 } \) = Rs.  480
(iii) Rate of interest received by him on his money
\(=\frac{\text {Income}}{\text {Investment}}\times100=\frac{480}{5000}\times100=9.6\%\)

Step 1: For 20% stocks:
F.V. = Rs. 100
Income = \(\frac{20}{100}\times 10000\)
= Rs. 2,000 ......(1)
Investment = Rs. 10,000
Face value = Rs. 100
Market value = Rs. 100 + 42 – 2 = 140
Number of shares = \(\frac{Investments}{FV}\)
= \(\frac{10,000}{100}\) = 100
Sales proceeds = 100 × 140 = 14,000
Step 2: For 15% stocks:
M.V. = Rs. 100 – 22 + 2 = 80
Number of shares = \(\frac{Investments}{FV}\)
= \(\frac{14000}{80}\) = 175
Income = 175 x \(\frac{15}{100} \times 100\) = Rs. 2625
Step 3: Change of income:
Change of income = Rs. 2625 – Rs. 2000 = Rs. 625

F.V. = Rs 10
Total face value of preference shares = Rs.1,00,000 \(\times\) 10 = Rs.10,00,000
Total face value of ordinary shares = Rs.50,000 \(\times\) 10 = Rs.5,00,000
Total dividend amount paid to shareholders = Rs.(3,20,000 – 40,000 – 20,000) = Rs.2,60,000
Dividend for preference shares = \(\frac{16}{100}\times 10,00,000\) = Rs 1,60,000
Dividend to ordinary shares = 2,60,000 – 1,60,000 = Rs 1,00,000
Dividend rate for ordinary share = \(\frac{Income}{investment}\times 100\%\)
Dividend = \(\frac{1,00,000}{5,00,000}\times 100\) = 20%.

If F.V = 100, Investment = 90
FV 10,000,
Investment \(= \frac{ 90 \times 10,000}{100} = 9000\)

If FV 100, Investment = 120
FV = 20,000,
Investment = \(\frac{120\times 20,000}{100} \) = Rs. 24000

Investment = 200 x 100 x \(\frac{8}{100}\)= Rs. 1600