Table of Contents
How to find Compound Interest when Interest is Compounded Quarterly?
If the Rate of Interest is Annual and Interest is Compounded Quarterly then the number of years is multiplied by 4 i.e. 4n and the annual interest rate is cut down by one-fourth. In such cases, Formula for Quarterly Compound Interest is given as under
Let us assume the Principal = P, Rate of Interest = r/4 %, and time = 4n, Amount = A, Compound Interest = CI then
A = P(1+(r/4)/100)4n
In the above formula rate of interest is divided by 4 whereas the time is multiplied by 4.
We know CI = A – P
= P(1+(r/4)/100)4n – P
= P{1+(r/4)/100)4n – 1}
If you are aware of any of the three then you can automatically find the other one.
Solved Problems on finding Compound Interest when Compounded Quarterly
1. Find the compound interest when $1,00, 000 is invested for 6 months at 5 % per annum, compounded quarterly?
Solution:
Principal Amount = $1,00, 000
Rate of Interest = 5% per annum
n = 6 months = 1/2 year
Since Interest Rate is Compounded Quarterly divide the interest rate by 4 i.e. r/4 and multiply the time by 4 i.e. 4n
Amount A = P(1+(r/4)/100)4n
Substitute the Inputs in the above formula to find the amount
A = 1,00,000(1+(5/4)/100)4*1/2
= 1,00,000(1+5/400)2
= $ 1,02,515
CI = A – P
= $ 1,02,515 – $ 1,00,000
=$2515
2. Find the amount and the compound interest on Rs. 12,000 compounded quarterly for 9 months at the rate of 10% per annum?
Solution:
Principal Amount = Rs.12, 000
Rate of Interest = 10% per annum
n = 9 months = 9/12 = 3/4 year
Since Interest Rate is Compounded Quarterly divide the interest rate by 4 i.e. r/4 and multiply the time by 4 i.e. 4n
Amount A = P(1+(r/4)/100)4n
Substitute the Input Values in the above formula to find the amount
A= 12,000(1+(10/4)/100)4*3/4
= 12,000(1+10/400)3
= 12,000(1+0.025)3
= 12,000(1.025)3
= Rs. 12922
CI = A – P
= 12922 – 12000
= Rs. 922
3. Calculate the compound interest (CI) on Rs. 4000 for 1 year at 10% per annum compounded quarterly?
Solution:
Principal Amount = Rs. 4,000
Rate of Interest = 10% per annum = 10/4 %
n = 1 year
Since Interest Rate is Compounded Quarterly divide the interest rate by 4 i.e. r/4 and multiply the time by 4 i.e. 4n
Amount A = P(1+(r/4)/100)4n
Substitute the Input Values in the above formula to find the amount
A = 4000(1+(10/4)/100)4*1
= 4000(1+10/400)4
= 4000(1.1038)
= Rs. 4415.25
CI = A – P
= 4415.25 – 4000
= Rs. 415.25
