Calculation of Compound Interest on Rs 80000 for 8 months at 20% p.a. payable quarterly:

To calculate the compound interest on Rs 80000 for 8 months at 20% p.a. payable quarterly, we need to first determine the quarterly interest rate, which can be calculated as follows:

Quarterly interest rate = Annual interest rate / 4
= 20% / 4
= 5%

Now, we can use the formula for compound interest to calculate the interest earned on Rs 80000 for 8 months, payable quarterly:

Compound interest = P [(1 + r/n)^(nt) - 1]
Where,
P = Principal amount (Rs 80000)
r = Annual interest rate (20%)
n = Number of times interest is compounded in a year (4)
t = Time period (8/12 years)

Substituting the values in the formula, we get:

Compound interest = 80000 [(1 + 0.05/4)^(4*(8/12)) - 1]
= 80000 [(1 + 0.0125)^1.33 - 1]
= 80000 [1.015^1.33 - 1]
= 80000 [0.021]
= Rs 1680

Therefore, the compound interest earned on Rs 80000 for 8 months at 20% p.a., payable quarterly, is Rs 1680.

Explanation:

Compound interest is the interest earned on the principal amount as well as on the interest earned in previous periods. In this case, the interest is compounded quarterly, which means that the interest earned in each quarter is added to the principal amount, and interest is then calculated on the new total for the next quarter.

To calculate the compound interest, we first determined the quarterly interest rate by dividing the annual interest rate by 4. We then used the formula for compound interest, which takes into account the principal amount, the interest rate, the number of times interest is compounded in a year, and the time period for which the interest is being calculated.

By substituting the values in the formula, we calculated the compound interest earned on Rs 80000 for 8 months, payable quarterly, which came out to be Rs 1680. This means that the total amount due after 8 months would be Rs 80000 + Rs 1680 = Rs 81680.