What sum will amount to Rs. 4913 in 18 months, if the rate of interest

1.	What sum will amount to Rs. 4913 in 18 months, if the rate of interest is 12 1/2% per annum, compounded half-yearly?
Answer» Given, Amount = Rs.4913 Time = 18 months \(=\frac{18}{12}\) years \(=\frac{3}{2}\times2\) = 3 half yearly Rate \(={12}\frac{1}{2}\text%\) \(=\frac{25}{2}\text%\) \(=\frac{25}{4}\text%\) half yearly Let principal = P So, \({A}={P}[({1}+\frac{R}{100})^T]\) \(={P}({1}+\frac{25}{4\times100})^3]\) = 4913 \(={P}[(\frac{17}{16})^3]\) = 4913 \(={P}\times\frac{4913}{4096}\) 4913 \(={P}=\frac{4913\times4096}{4913}\) = Rs.4096 Hence , Principal = Rs. 4096

What sum will amount to Rs. 4913 in 18 months, if the rate of interest is 12 1/2% per annum, compounded half-yearly?

Answer»

Given,

Amount = Rs.4913

Time = 18 months \(=\frac{18}{12}\) years

\(=\frac{3}{2}\times2\) = 3 half yearly

Rate \(={12}\frac{1}{2}\text%\) \(=\frac{25}{2}\text%\)

\(=\frac{25}{4}\text%\) half yearly

Let principal = P

So,

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

\(={P}({1}+\frac{25}{4\times100})^3]\) = 4913

\(={P}[(\frac{17}{16})^3]\) = 4913

\(={P}\times\frac{4913}{4096}\) 4913

\(={P}=\frac{4913\times4096}{4913}\) = Rs.4096

Hence ,

Principal = Rs. 4096