find the difference between the c.i on rs 120000 for 1 year at 20% pa compounded half yearly and quaterly.
pls give relevant answer
Answers
Answer:
P = initial amount in Rupees = 120000
R = rate of interest per cent per year = 20
T = time period in years = 1
m = compounding interval
A = final amount at the end of period T
CI = Compound interest = A - P
A = P*(1 + R/m/100)mT
A = P*(1 + (R/m)/100))^(mT) ............(i)
Case 1:
m = 2 (half-yearly compounding means two intervals in a year)
mT = 2*1 = 2
R/m = 20/2 = 10
=> A = 120000*(1 + 10/100)^2
=> A = 120000*(1.1)^2
=> A = 120000*1.21
=> A = 145200
CI = A - P
CI = 145200 - 120000 = 25200 ..........(i)
Case 2:
m = 4 (quarterly compounding means four intervals in a year)
mT = 4*1 = 4
R/m = 20/4 = 5
=> A = 120000*(1 + 5/100)^4
=> A = 120000*(1.05)^4
=> A = 120000*(1.215506)
=> A = 145860.75
CI = A - P
CI = 145860.75 - 120000 = 25860.75 ..........(ii)
Difference in CI in the two cases
= 25860.75 - 25200
= 660.75
Hope this is helpful for you.