what is the difference between the compound interests on rs. 5000 for 1 years at 4% per annum compounded yearly and half-yearly?
Answer: To calculate the difference between the compound interests on Rs. 5000 for 1 year at 4% per annum compounded yearly and half-yearly, we can use the formula:
A = P(1 + r/n)^(n*t)
where:
A = the amount after t years
P = the principal amount
r = the annual interest rate
n = the number of times the interest is compounded in a year
t = the time in years
For yearly compounding, we have:
P = Rs. 5000
r = 4% per annum
n = 1 (compounded yearly)
t = 1 year
So, the amount after 1 year is:
A1 = 5000(1 + 0.04/1)^(1*1)
= 5200
For half-yearly compounding, we have:
P = Rs. 5000
r = 4% per annum
n = 2 (compounded half-yearly)
t = 1 year
So, the amount after 1 year is:
A2 = 5000(1 + 0.04/2)^(2*1)
= 5204
The difference in compound interest is the difference between the two amounts:
Difference = A2 - A1
= 5204 - 5200
= 4
Therefore, the difference in compound interest between yearly and half-yearly compounding on Rs. 5000 for 1 year at 4% per annum is Rs. 4.