**Calculation of Compound Interest:**

To calculate the compound interest, we can use the formula:

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

Where:
A = the future value of the investment/loan, including interest
P = the principal investment amount (initial deposit)
r = annual interest rate (as a decimal)
n = number of times that interest is compounded per year
t = number of years the money is invested/borrowed for

In this case, Manisha deposited Rs. 1000 at an annual interest rate of 5% for 3 years with the State Bank of India. Let's calculate the compound interest and the amount she will get back at the expiry of the period.

**Calculation:**

Given:
P = Rs. 1000
r = 5% = 0.05 (as a decimal)
n = 1 (compounded annually)
t = 3 years

Substituting these values into the formula:

A = 1000(1 + 0.05/1)^(1*3)
A = 1000(1 + 0.05)^3
A = 1000(1.05)^3
A ≈ Rs. 1157.63

**Explanation:**

At the expiry of the 3-year period, Manisha will get back approximately Rs. 1157.63.

Compound interest is calculated based on the initial principal amount and the accumulated interest over the investment period. Unlike simple interest, compound interest takes into account the interest earned in previous periods, leading to exponential growth.

In this case, Manisha's initial deposit of Rs. 1000 earns an annual interest rate of 5%. Since the interest is compounded annually, the interest is added to the principal amount at the end of each year. As a result, the interest earned in each subsequent year also contributes to the overall growth of the investment.

After 3 years, the compound interest has amounted to approximately Rs. 157.63, resulting in a total investment value of approximately Rs. 1157.63.

Therefore, at the expiry of the period, Manisha will get back Rs. 1157.63, which includes the initial principal amount and the compound interest earned over 3 years.