Market value of 325 shares
= No. of. shares x M.V of 1 share
= 62 x 132 = Rs. 8184

Let ‘x’ be the number of shares.
Face Value = Rs. 100
Face value of ‘x’ shares = Rs. 100x
\(\frac{12}{100}\times 100x=Rs. 3600\)
12 x = 3600 \(\Rightarrow\) x = 300
Hence the number of shares = 300

Let x be the number of shares.
Face value of ‘x’ shares = Rs. 25 x
Now \(\frac{10}{100}\times 25x=Rs. 2,000\)
\(\Rightarrow x=\frac{2000\times 100}{25\times 10}=800\)
Hence the number of shares = 800

Here a = 64,000, n = 12 and i = \(\frac{10}{100}=0.1\)
Amount of Ordinary annuity (A) = \(\frac{a}{i}[(1+i)^n-1]\)
= \(\frac{64000}{0.1}[(1+0.1)^{12}-1]\)
= 6,40,000 [(1.1)¹² – 1]
= 6,40,000[3.3184 – 1]
= 6,40,000 [2.3184]
= 64 x 23184
∴ A  = Rs. 14,83,776.

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 Investment in each stock be 120 x 135
At 7% stock
Investment = 120, Income = 7
Investment = 120 x 135
Income = \(\cfrac { 7\times120\times135 }{ 120 }=Rs.945\)
At 8% stock
Investment = 135, Income = 8
Investment = 120 x 135
Income =\(\cfrac { 8 \times 120 \times135 }{ 135 }=Rs.960\)
\(\therefore\) 8% of Rs.100 shares at Rs.135 is a better investment .

a = Rs.5000, i = \(\frac{10}{100}\) = 0.1, n = 12
\(A=\frac { a(1+i) }{ i } \left[ (1+i)^{ n }-1 \right] \)
\( \left[ \left( 1.1 \right) ^{ 12 }=3.1384 \right] \)
=\(\cfrac { 5000\left( 1.1 \right) }{ 0.1 } \left[ \left( 1.1 \right) ^{ 12 }-1 \right] \)
= 55,000 [3.1384 - 1]
= 55,000 [2.1384]
= Rs. 1,17,612

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

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.

Here A = 1,67,160, n = 16 i = \(\frac{15}{100}=0.15\) a = ?
To find: a
Now A = \(\frac{a}{i}[(1+i)^n-1]\)
1,67,160 = \(\frac{a}{0.15}[(1+0.15)^{16}-1]\)
= \(\frac{a}{15}[(1.15)^{16}-1]\)
⇒ a = \(\frac{1,67,160\times 0.15}{(1.15)^{16}-1}\)
a = \(\frac{1,67,160\times 0.15}{9.358-1}\)
= \(\frac{1,67,160\times 0.15}{8.358}\)
= 3,000
Therefore a = Rs.3,000

Number of preference shares = 1000
Preferential stock = 1000 X 100 = Rs.1,00,000
Ordinary shares = 4000
Ordinary shares = 4000 x 100 = Rs.4,00,000
Total dividend = Rs.40,000
Dividend on preference share=\(\frac { 1,00,000 }{ 100 } \) x 6 = Rs.6,000
Dividend on ordinary shares=Total dividend-dividend on preference shares
= 40,000-6000
=Rs.34,000
Sundar's income on preference shares
= No.of shares X FV XRate percentage
=100 x 100 x \(\frac { 6 }{ 100 } \)
=Rs.600         ...(1)
Sundar's income on ordinary shares
=\(\frac { 2500 \times 100 }{ 4,00,000 } \) x 34,000=Rs.1700   ..(2)
\(\therefore\)Sundar's total income = 600+1700
= Rs.2300

Given a = Rs.75, i=\(\cfrac { 8 }{ 12 } \)% = 4% = 0.004,n = 10 X 2 =20
A = \(\cfrac { a }{ i } \left[ \left( 1+i \right) ^{ n }-1 \right] \)
=\(\cfrac { 75 }{ 0.04 } \) [(1.04)²⁰-1]
=1875 (2.1878-1)
= 1875(1.878)
= Rs.2227
(1.04)⁴⁰ = 20 log (1.04)
= 20(0.0170)
= 0.34
Antilog of 0.34 is 2.1878

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

\(P =\frac{\frac{a}{i}}{k} \)
\(=\frac{\frac{2000}{0.1}}{12}=2,40,000\)

\(x=\frac{12 \times 96}{10}=115.20\)

Investment = 80, Income = 7
Investment = 100,
Income \(= \frac{ 7 \times 100}{80} = 8.75 \%\)

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