Find the rate percent per annum if Rs. 2000 amount to Rs. 2662 in 1 1/

1.	Find the rate percent per annum if Rs. 2000 amount to Rs. 2662 in 1 1/2 years, interest being compounded half-yearly?
Answer» Given, Principal = Rs.2000 Amount = Rs.2662 Time \(={1}\frac{1}{2}\) years \(=\frac{3}{2}\times2\) = 3 half years Let rate = R% per annum, \(\frac{R}{2}\text%\) half yearly So, A = \({P}[({1}+\frac{R}{100})^T]\) \(={2000}[({1}+\frac{R}{2\times100})^3]\) = 2662 \(=({1}+\frac{R}{100})^3\) \(=\frac{2662}{2000}\) \(=\frac{1331}{1000}\) \(=(\frac{11}{10})^3\) \(={1}+\frac{R}{200}\) \(=\frac{11}{10}\) \(=\frac{R}{200}\) \(=\frac{11}{10}-{1}\) \(=\frac{1}{10}\) = R \(=\frac{1\times200}{10}\) = 20% per annum Hence , Rate = 20% per annum

Find the rate percent per annum if Rs. 2000 amount to Rs. 2662 in 1 1/2 years, interest being compounded half-yearly?

Answer»

Given,

Principal = Rs.2000

Amount = Rs.2662

Time \(={1}\frac{1}{2}\) years \(=\frac{3}{2}\times2\) = 3 half years

Let rate = R% per annum, \(\frac{R}{2}\text%\) half yearly

So,

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

\(={2000}[({1}+\frac{R}{2\times100})^3]\) = 2662

\(=({1}+\frac{R}{100})^3\) \(=\frac{2662}{2000}\) \(=\frac{1331}{1000}\) \(=(\frac{11}{10})^3\)

\(={1}+\frac{R}{200}\) \(=\frac{11}{10}\)

\(=\frac{R}{200}\) \(=\frac{11}{10}-{1}\) \(=\frac{1}{10}\)

= R \(=\frac{1\times200}{10}\) = 20% per annum

Hence ,

Rate = 20% per annum