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in Compound Interest by (28.9k points)
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In what time will Rs. 4400 become Rs. 4576 at 8% per annum interest compounded half-yearly?

1 Answer

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Best answer

Given, 

Principal = Rs. 4400 

Amount = Rs.4576 

Rate = 8% p.a \(=\frac{8}{2} ={4}\text%\) half yearly

Let time = T years = 2T half years 

So,

\(={P}[({1}+\frac{4}{100})^T]\)

\(={4400}[({1}+\frac{4}{100})^{2T}]\) = 4576

\(=(\frac{26}{25})^{2T}\) \(=\frac{4576}{4400}\) \(=\frac{26}{25}\)

= 2T = 1

\(={T}=\frac{1}{2}\) years

Hence, 

Time \(=\frac{1}{2}\) years

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