Given annual income =Rs.1200
No.of shares =150
FV= 100
Annual income = No.of shares x FV x Rate percentage
1200=150 x 100 x\(\cfrac { r }{ 100 } \)
\(\cfrac { 1200 }{ 150 } =r\Rightarrow r=8%\)%

Given a = Rs.1000,i = 7% = 0.07.n = 5
A = \(\cfrac { a }{ i } \left[ \left( 1+i \right) ^{ n }-1 \right] \)
=\(\cfrac { 1000 }{ 0.07 } \) x [(1.07)⁵-1]
=14,285.71[1.4028-1]
= (14,285.71)[0.4028]
= Rs.5754.28
(1.07)⁵ = 5 log(1.07)
= 5(0.0294)
= 0.1470
Antilog of 0.1470 is 1.4028

Given a = Rs.1000,r = \(\cfrac { 8 }{ 100 } \times \cfrac { 1 }{ 4 } \) = 0.02,n =3 X 4 = 12
A =\(\cfrac { a }{ i } \left( 1+i \right) \left[ \left( 1+i \right) ^{ n }-1 \right] \)
=\(\cfrac { 1000 }{ 0.02 } \left( 1.02 \right) \left[ \left( 1.02 \right) ^{ 12 }-1 \right] \)
= 51,000[1.269-1]
= 51,000[0.269]=Rs.13,719
(1.02)¹² = 12log(1.02)
=12(0.0086)
= 0.1032
Antilog of 0.1032 is 1.269

Cost of one share = 100-4 = 96
Stock = 9300
Number of shares purchased = \(\frac { \text {Stock }}{ FV } \)
=\(\frac { 9300 }{ 100 } \) = 93
\(\therefore\)  Purchase price of 93 shares = 93 x 96 = Rs.8928

Dividend rate =8%
Annual income =Rs.80
Stock=\(\frac { \text {Annual income }}{\text { Dividend Rate } }\)X100
=\(\frac { 80 }{ 8 } \) x 100 = Rs.1000

a = Rs.2000,i =\(\frac { 6 }{ 1200} \) = 0.005, n = 5 x 12 = 60
P = \(\frac { a }{ i } \left[ \left( 1+i \right) ^{ n }-1 \right] \)
= \(\frac { 2000 }{ 0.005 } \left[ \left( 1.005 \right) ^{ 60 }-1 \right] \)
= 400000 [1.3489 - 1]
= 400000 (0.3489)
= Rs. 1,39,560

A = 30,200 i = \(\frac{8}{400}\) = 0.02, n = 10 x 4 = 40
A = \(\cfrac { a }{ i } \left[ \left( 1+i \right) ^{ n }-1 \right] \)
30,200 ​\( =\cfrac { a }{ 0.02 } \left[ \left( 1.02 \right) ^{ 40 }-1 \right] \)
30,200 x 0.02 = a[2.2080-1]   
a =​​​​​​ ​\(\cfrac { 604 }{ 1.2080 } \) = Rs. 500

a = Rs 1500, i = \(\frac { 12 }{ 12 \times 100} \) = 0.01, n = 12.
A = \(\cfrac { a }{ i } \left[ \left( 1+i \right) ^{ n }-1 \right] \)
\(=\cfrac { 500 }{ 0.01 } \left[ \left( 1.01 \right) ^{ 12 }-1 \right] \)
= 150000 [1.262-1]  
= 150000 [0.1262]
= Rs. 18,930

Number of shares = \(\frac { 4500 }{ 10 } \) = 450
Annual income = No.of shares x F.V x Rate of dividend
= 450 x 10 x \(\frac { 2 }{ 100 } \) = Rs. 540
S.P of 450 shares = 450 x 23 = Rs. 10,350   
Number of shares bought \(=\frac { 10,350 }{ 18 } =575\)
Income = \(575 \times 25\times \frac { 10 }{ 100 } =Rs.1437.50\) 
Change in his income = 1437.50 - 540 
= Rs. 897.50

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
\(=\frac{\text {Income}}{\text {Investment}}\times100=\frac{480}{5000}\times100=9.6\%\)