Find the difference between compound interest payable annually and half annually for a amount Rs 14000 at the rate 12% per annum for 2 years

14000(1+.12)^2

vs
14000(1+.12/2)^(2*2)

Ci=3561.6,half annually compound interest=3674.67

To find the difference in compound interest payable annually and half annually, we can use the formula for compound interest:

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

Where:
A = the final amount after interest
P = the principal amount
r = the annual interest rate (in decimal form)
n = the number of compounding periods per year
t = the number of years

For compound interest payable annually:
P = Rs 14,000
r = 12% per annum = 0.12
n = 1 (since it is compounded annually)
t = 2 years

Using the formula, we can calculate the final amount (A) for this case:

A_annual = 14000(1 + 0.12/1)^(1*2)
= 14000(1 + 0.12)^2
= 14000(1.12)^2
= 14000(1.2544)
= Rs 17,561.60

Now, let's calculate compound interest payable half annually:
P = Rs 14,000
r = 12% per annum = 0.12
n = 2 (since it is compounded half annually, twice a year)
t = 2 years

Using the formula, we can calculate the final amount (A) for this case:

A_half_annual = 14000(1 + 0.12/2)^(2*2)
= 14000(1 + 0.12/2)^4
= 14000(1 + 0.06)^4
= 14000(1.06)^4
= Rs 17,750.56

Now, to find the difference in compound interest, we subtract the amount accumulated on the annual basis from the amount accumulated on the half-annual basis:

Difference = A_half_annual - A_annual
= Rs 17,750.56 - Rs 17,561.60
= Rs 188.96

Therefore, the difference in compound interest payable annually and half annually for an amount of Rs 14,000 at the rate of 12% per annum for 2 years is Rs 188.96.