Compound Interest (Quarterly by Shortcut Method) at Algebra Den

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Home >> Simple Interest >> Compound Interest >> Calculate Compound Interest (Quarterly) >>

Compound Interest (Quarterly by Shortcut Method)

Calculate Compound Interest (half yearly) Calculate Compound Interest (Quarterly) Difference Compound Interest Yearly & Half Yearly Difference Compound Interest Yearly & Quarterly Difference Compound Interest Half Yearly & Quarterly

Before you study How to calculate Compound Interest where rate of interest is compounded quarterly, you are advice to read:

How to calculate compound interest yearly ?
How to calculate compound interest half yearly ?

In general we can say that: In Compound Interest where rate of interest is compounded quarterly, interest is calculated after every 3 months

Or we can also that:
In Compound Interest (compounded quarterly) interest is added after every 3 months to form a new principal.

Formula to Calculate Amount in case of compound interest compounded half yearly:
Amount = P ( 1 + R/400 ) ^4T

Here:
P is Principal
R is Rate of Interest
T is Time in years

Formula to Calculate compound interest when rate compounded half yearly:
CI = P [ ( 1 + R/400 ) ^4T - 1]

Example : Find Compound interest on $10000 for 1 year at rate 10% interest per annum compounded semi annually ?
Solution: As per the given question:

Principal or P = $10000
Rate of Interest or R = 10%
Time or T= 1 year

CI = P [ ( 1 + R/400 ) ^2T - 1]

Put values of P, R and T from above and we get:
CI = 10000 [ ( 1 + 10 / 400 ) ^{4 X 1} - 1 ]

Solution as shown in below steps:
CI = 10000 [ ( 1 + 10 / 400 ) ⁴ - 1 ]
CI = 10000 [ { ( 400 + 10) / 400 } ⁴ - 1 ]
CI = 10000 [ { 410 / 400 } ⁴ - 1 ]
CI = 10000 [ { 41 / 40 } ⁴ - 1 ]
CI = 10000 [ { 2825761 / 2560000 } - 1 ]
CI = 10000 [ (2825761 -2560000) / 2560000 ]
CI = 10000 [ 265761 / 2560000 ]
CI = 10000 X 265761 / 2560000
CI = 265761 / 256
CI = 1038.13

Hence, compound interest; when rate is compounded quarterly; is equal to $1038.13.