Calculation of Gain in Rupees when Compounded Quarterly

To calculate the gain in rupees when compounded quarterly, we can use the following formula:

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

Where:
A = the amount after t years
P = the principal amount
r = the nominal annual interest rate
n = the number of times the interest is compounded per year
t = the number of years

In this case, let's assume that the principal amount is Rs. 10,000 and the interest rate is 4.5% per annum. Since the interest is compounded quarterly, we have:

n = 4 (quarterly)
r = 4.5% per annum
t = 1 year

Plugging these values into the formula, we get:

A = 10,000 (1 + 0.045/4)^(4*1)
A = 10,463.12

Therefore, when compounded quarterly, the amount after one year is Rs. 10,463.12. The gain in rupees is:

Gain = A - P
Gain = 10,463.12 - 10,000
Gain = 463.12

Calculation of Gain in Rupees when Compounded Annually

To calculate the gain in rupees when compounded annually, we can use the same formula as above, but with n = 1 (annually). Therefore, we have:

n = 1 (annually)
r = 4.5% per annum
t = 1 year

Plugging these values into the formula, we get:

A = 10,000 (1 + 0.045/1)^(1*1)
A = 10,450.00

Therefore, when compounded annually, the amount after one year is Rs. 10,450.00. The gain in rupees is:

Gain = A - P
Gain = 10,450.00 - 10,000
Gain = 450.00

Comparison of Gain in Rupees

When we compare the gain in rupees when compounded quarterly and annually, we see that:

- When compounded quarterly, the gain is Rs. 463.12
- When compounded annually, the gain is Rs. 450.00

Therefore, the gain is higher when compounded quarterly as compared to annually. This is because when the interest is compounded more frequently, the effective interest rate is higher, which leads to a higher gain.