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What is the equivalent rate fo compound ...

What is the equivalent rate fo compound interest per annum if the half yearly compound interest be 10%?

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Let the principal be Rs. x.
`:.` The amount of Rs. x in 1 year at the rate of compound interest 10% compounded half yearly
`=Rs. x xx(1+(10/2)/100)^(2xx1)`
`=Rs.x xx(1+1/20)^(2)=Rs.x xx(21/20)^(2)=Rs.(441x)/440`
Let the equivalent rate be r% .
`:.x(1+r/100)^(1)=(441x)/400impliesr/100=441/400-1`
`impliesr/100=(441-400)/400`
`impliesr/100=41/400`
`impliesr=41/4=10.25`
Hence the required equivaletn rate `=10.25%` per annum.
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