Calculating Compound Interest

To calculate the compound interest earned on an amount, we use the formula:

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

Where:
A = the final amount including the interest
P = the principal amount (initial investment)
r = the annual interest rate (as a decimal)
n = the number of times that interest is compounded per year
t = the number of years

In this case, we have:
P = Rs. 1800
r = 8% per annum (0.08 as a decimal)
n = 4 (quarterly compounding)
t = 1 year

Calculating the Compound Interest

Let's substitute the given values into the formula and calculate the compound interest earned:

A = 1800(1 + 0.08/4)^(4*1)
A = 1800(1 + 0.02)^4
A = 1800(1.02)^4
A ≈ 1800(1.082432)
A ≈ Rs. 1948.37

Therefore, the final amount after 1 year would be approximately Rs. 1948.37.

Calculating the Compound Interest Earned

To find the compound interest earned, we subtract the principal amount from the final amount:

Compound Interest = A - P
Compound Interest = 1948.37 - 1800
Compound Interest ≈ Rs. 148.37

Therefore, the compound interest earned at the end of 1 year would be approximately Rs. 148.37.

Summary:

- Principal amount (P): Rs. 1800
- Annual interest rate (r): 8% per annum
- Number of times compounded per year (n): 4 (quarterly compounding)
- Number of years (t): 1 year
- Final amount (A): Rs. 1948.37
- Compound interest earned: Rs. 148.37