To calculate the compound interest on Rs 16000 at 20% per annum for 9 months, compounded quarterly, we need first to calculate the quarterly interest rate and the number of compounding periods.
Quarterly interest rate = Annual interest rate / 4
= 20% / 4
= 5%
Number of compounding periods = (Time in months) / (Number of months per compounding period)
= 9 / 3
= 3
Using the formula for compound interest:
A = P(1 + r/n)^(nt)
where,
A = final amount
P = principal amount
r = annual interest rate
n = number of compounding periods per year
t = time in years
Plugging in the values, we get:
A = 16000(1 + 0.05/4)^(4*3/12)
A = 16000(1 + 0.0125)^1
A = 16000(1.0125)
A = 16180
Therefore, the compound interest on Rs 16000 at 20% per annum for 9 months, compounded quarterly is Rs 1800 (i.e., A - P = 16180 - 16000).