In what time will Rs. 4400 become Rs. 4576 at 8% per annum interest co

1.	In what time will Rs. 4400 become Rs. 4576 at 8% per annum interest compounded half-yearly?
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, A \(={P}[({1}+\frac{4}{100})^T]\) \(={4400}[({1}+\frac{4}{100})^{2T}]\) = 4576 \(=(\frac{26}{25})^{2T}\) \(=\frac{4576}{4400}\) \(=\frac{26}{25}\) = 2T = 1 \(={T}=\frac{1}{2}\) years Hence, Time \(=\frac{1}{2}\) years

In what time will Rs. 4400 become Rs. 4576 at 8% per annum interest compounded half-yearly?

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,

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

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

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

= 2T = 1

\(={T}=\frac{1}{2}\) years

Hence,

Time \(=\frac{1}{2}\) years