Let the sum be Rs. P
P{ 1 + 8 100 2- 1 } = 2828.80

It is in the form of   a 2 - b 2 = a + b a - b

P(8/100)(2 + 8/100) = 2828.80

P = 2828.80 / (0.08)(2.08)

= 1360/0.08 = 17000

Principal + Interest = Rs. 19828.80

Given principal amount = Rs. 8000

Time = 3yrs

Rate = 5%

C.I for 3 yrs =  $$\begin{gathered} 8000 x 105 100 x 105 100 x 105 100 - 8000 \\ = Rs . 1261 \end{gathered}$$

Now, C.I for 2 yrs =  $$\begin{gathered} 8000 x 105 100 x 105 100 \\ = Rs . 820 \end{gathered}$$

Hence, the required difference in C.I is 1261 - 820 = Rs. 441

C.I. when interest
compounded yearly=rs.[5000*(1+4/100)(1+1/2*4/100)]

= Rs. 5304.

C.I. when interest is
compounded half-yearly=rs.5000(1+2/100)^3

= Rs. 5306.04
Difference = Rs. (5306.04 - 5304) = Rs. 2.04

We know that,

$$\begin{gathered} S . I . = PTR 100 \\ ? P = S . I x 100 T x R \\ And also , \\ C . I = P 1 + R 100 n - 1 \end{gathered}$$

From given data, P = Rs. 8625

Now, C.I  =  $$\begin{gathered} 8625 1 + 4 100 2 - 1 \\ = 8625 26 25 2 - 1 \\ = 8625 676 625 - 1 \\ = 8625 x 51 625 \\ C . I = Rs . 703 . 80 \end{gathered}$$

C.I =  P 1 + r 100 t - 1

594.5 =  5800 1 + r 100 2 - 1

  594 . 5 5800 + 1 = 1 + r 100 2

r 100 = 1 . 05 - 1 = 0 . 05 = > r = 5 % .

P 1 + 20 100 n > 2P 

Now, (6/5 x 6/5 x 6/5 x 6/5) > 2.

So, n = 4 years.

Let the rate be R% p.a. Then,

1800 1 + R 100 2 - 1800 - 1800 * R * 2 100 = 405

1800 100 + R 2 10000 - 1 - 2 R 100 = 405

  1800 100 + R 2 - 10000 - 200 R 10000 = 405

?

9 5 * R 2 = 405 ? R 2 = 405 * 5 9 = 225 ? R = 15 
Rate = 15%.

Rs.100 invested in compound interest becomes Rs.200 in 5 years.

The amount will double again in another 5 years.

i.e., the amount will become Rs.400 in another 5 years.

So, to earn another Rs.200 interest, it will take another 5 years.

Let the sum be Rs. x. Then,

  C . I = x * 50 300 * 100 3 - x = 343 x 216 - x = 127 x 216 

? 127 x 216 = 1270 

x = 2160 

Thus, the sum is Rs. 2160

  S . I = R s . 2160 * 50 3 * 3 * 1 100 = R s 1080

Amount

=Rs.[8000x(1+5/100)²]

= Rs.[8000 x 21/20x21/20]

= Rs.8820.