Amount =  Rs. \(\left[25000\times\left(1+\frac{12}{100}\right)^{3}\right]\)

= Rs. \(\left(25000\times\frac{28}{25}\times\frac{28}{25}\times\frac{28}{25}\right)\)

= Rs. 35123.20

So, C.I. = Rs. (35123.20 - 25000) = Rs. 10123.20

Let the rate be R% p.a.

Then, \(1200\times\left(1+\frac{R}{100}\right)^{2}=1348.32\)

\(\Rightarrow\left(1+\frac{R}{100}\right)^{2}=\frac{134832}{120000}=\frac{11236}{10000}\)

So,  \(\left(1+\frac{R}{100}\right)^{2} = \left(\frac{106}{100}\right)^{2}\)

\(1+\frac{R}{100} =\frac{106}{100}\)

R = 6%

P \(\left(1+\frac{20}{100}\right)^{n}>2P \Rightarrow\left(\frac{6}{5}\right)^{n}> 2.\)

Now,  \(\left(\frac{6}{5}\times\frac{6}{5}\times\frac{6}{5}\right)>2.\)

So n  = 4 year

Amount = Rs. \(\left[8000\times\left(1+\frac{5}{100}\right)^{2}\right]\)

= Rs. \(\left(8000\times\frac{21}{20}\times\frac{21}{20}\right)\)

= Rs. 8820.

Amount of Rs. 100 for 1 year 
when compounded half-yearly = \(Rs. \left[100\times\left(1+\frac{3}{100}\right)^{2}\right] = Rs. 106.09\)

So, Effective rate = (106.09 - 100)% = 6.09%

C.I. = Rs. \(\left[4000\times\left(1+\frac{10}{100}\right)^{2}-4000\right]\)

= Rs.\(\left(4000\times\frac{11}{10}\times\frac{11}{10}-4000\right)\)

= Rs. 840.

Sum = Rs. \(\left(\frac{420\times100}{3\times8}\right)= Rs. 1750.\)

Sum = Rs. \(\left(\frac{50\times100}{2\times5}\right)= Rs. 500. \)

Amount  =  Rs.  \(\left[500\times\left(1+\frac{5}{100}\right)^{2}\right]\)

= Rs.  \(\left(500\times\frac{21}{20}\times\frac{21}{20}\right)\)

= Rs. 551.25

 So, C.I. = Rs. (551.25 - 500) = Rs. 51.25

S.I. = Rs \(\left(\frac{1200\times10\times1}{100}\right)= Rs. 120.
\)

C.I. = Rs. \(\left[1200\times\left(1+\frac{5}{100}\right)^{2}-1200\right]= Rs. 123.\)

So, Difference = Rs. (123 - 120) = Rs. 3.

\(\left[15000\times\left(1+\frac{R}{100}\right)^{2}-15000\right]-\left(\frac{15000\times R\times2}{100}\right)= 96.\)  

\(15000\left[\left(1+\frac{R}{100}\right)^{2}-1-\frac{2R}{100}\right]= 96. \)

\(15000\left[\frac{(100+R)^{2}-10000-(200\times R)}{10000}\right]=96.\)

R^{2 = \(\left(\frac{96\times2}{3}\right) = 64\)}

R =  8.

So, Rate = 8 %.

Let the sum be Rs. P.

Then , \(\left[P\left(1+\frac{10}{100}\right)^{2}-P\right] = 525\)

P  \(\left[\left(\frac{11}{10}\right)^{2}-1\right] = 525\)

P =  \(\left(\frac{525\times100}{21}\right) = 2500\)

So , Sum =  Rs. 2500.

So, S.I. = Rs. \(\left(\frac{2500\times5\times4}{100}\right) = 500.\)