principal =  A = 4913 , T = 3 , R = 4 1 3

P = A 1 + R 100 T

 = Rs.4096

Interest earned in scheme M =   

P 1 + 20 100 2 - 1 = 11 P 25

Interest earned in scheme N =  

P x k x 2 100 = P k 50

Now, from the given data,

11 P 25 = 2 x P k 50

k = 11

Present Worth

= P 1 + R 100 2

= 169 1 + 4 100 2

= Rs.156.25

We know the formula for calculating

The compound interest  C = P 1 + r 100 n - 1 where P = amount, r = rate of interest, n = time

Here P = 5000, r1 = 10, r2 = 20

Then  $$\begin{gathered} C = 6500 1 + 10 100 2 x 1 + 20 100 2 - 1 \\ = 6500 x 1856 2500 \\ = 65 x 1856 25 \end{gathered}$$

C = Rs. 4826.

Let 'R%' be the rate of interest

From the given data,

$$\begin{gathered} 2520 2400 = 1 + R 100 4 1 + R 100 3 \\ ? 1 + R 100 = 63 60 \\ ? R = 5 \end{gathered}$$

Hence, the rate of interest R = 5% per annum.

Let Rs. K invested in each scheme

Two years C.I on 20% = 20 + 20 + 20x20/100 = 44%

Two years C.I on 15% = 15 + 15 + 15x15/100 = 32.25%

Now,

(P x 44/100) - (P x 32.25/100) = 528.75

=> 11.75 P = 52875

=> P = Rs. 4500

Hence, total invested money = P + P = 4500 + 4500 = Rs. 9000.

8000 × 33.1% = 2648

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