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Home >> Simple Interest >> Compound Interest >> Calculate Compound Interest (half yearly) >>

Compound Interest (half yearly 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 semi annually, you are advice to read:

What is Compound Interest ?

In general we can say that: In Compound Interest where rate of interest is compounded half yearly or semi annually, interest is calculated after every 6 months

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

  • Formula to Calculate Amount in case of compound interest compounded half yearly or semi-annually:
    Amount = P ( 1 + R / 200 ) 2T

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

  • Formula to Calculate compound interest when rate compounded half yearly or semi-annually:
    CI = P [ ( 1 + R / 200 ) 2T - 1]

    Example : Find Compound interest on $10000 for 2 years 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 = 2 years

    CI = P [ ( 1 + R/200 ) 2T - 1]

    Put values of P, R and T from above and we get:
    CI = 10000 [ (1 + 10/200) 2 X 2 - 1 ]

    Solution as shown in below steps:
    CI = 10000 [ ( 1 + 10 / 200 ) 4 - 1 ]
    CI = 10000 [ { (200 + 10) / 200) } 4 - 1 ]
    CI = 10000 [ { 210 / 200) } 4 - 1 ]
    CI = 10000 [ { 21 / 20) } 4 - 1 ]
    CI = 10000 [ { 194481 / 160000 } - 1 ]
    CI = 10000 [ (194481 - 160000) / 160000 ]
    CI = 10000 [ 34481 / 160000 ]
    CI = 10000 X 34481 / 160000
    CI = 34481 / 16
    CI = 2155.0625

    Hence, compound interest; when rate is compounded semi annually; is equal to $2155.0625.
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