Compound Amount:

The compound amount is the total value of an investment after a certain period of time, taking into account the interest earned on the principal amount. To calculate the compound amount, we use the formula:

A = P(1 + r/n)^(nt)

Where:
A = compound amount
P = principal amount (initial investment)
r = annual interest rate (in decimal form)
n = number of times interest is compounded per year
t = number of years

In this case, the principal amount is Rs. 1000, the annual interest rate is 6%, and the interest is compounded semi-annually for 6 years. Let's calculate the compound amount using the given formula:

A = 1000(1 + 0.06/2)^(2*6)
A = 1000(1 + 0.03)^(12)
A = 1000(1.03)^12

Now, the given information states that (1 + i)^n = 1.42576 for i = 3% and n = 12. We can use this information to simplify the calculation further.

(1 + i)^n = 1.42576
(1 + 0.03)^12 = 1.42576

So, (1.03)^12 = 1.42576

Now, substitute this value back into the compound amount formula:

A = 1000(1.42576)
A = 1425.76

Therefore, the compound amount after 6 years is Rs. 1425.76.

Compound Interest:

Compound interest is the difference between the compound amount and the principal amount. To calculate the compound interest, we subtract the principal amount from the compound amount.

Compound Interest = A - P
Compound Interest = 1425.76 - 1000
Compound Interest = Rs. 425.76

Therefore, the compound interest on Rs. 1000 at 6% compounded semi-annually for 6 years is Rs. 425.76.

In summary:
- Compound Amount: Rs. 1425.76
- Compound Interest: Rs. 425.76

1.42516×1000=1425.76