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

  P 1 + 20 100 n > 2 P ? 6 5 n > 2

  6 5 × 6 5 × 6 5 × 6 5 > 2

so, answer is 4 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

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.

when interest is reckoned using compound interest, interest being compounded annually. The difference in the simple interest and compound interest for two years is on account of the interest paid on the first year's interest  Hence 12% of simple interest = 90 => simple interest =90/0.12 =750.

As the simple interest for a year = 750 @ 12% p.a., the principal =750/0.12 = Rs.6250.

If the principal is 6250, then the amount outstanding at the end of 3 years = 6250 + 3(simple interest on 6250) + 3 (interest on simple interest) + 1 (interest on interest on interest) = 6250 +3(750) + 3(90) + 1(10.80) = 8780.80.

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.

Amount =  R s . 8000 * 1 + 5 100 2=Rs.8820