Question

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Q. In how much time in years an amount of Rs. 64,000 will become Rs. 68,921, if rate of interest is 5 % per annum, compounded half yearly?

Answer 1

Dear student,

$$\begin{gathered} PrincipalP=Rs64000 \\ Amount=Rs68921 \\ RateR=5\%for6month=halfyear \\ Forcompoundedhalfyearly \\ RateR=\frac{R}{2}=\frac{5\%}{2}=2.5\% \\ UsingA=P{\left(1+\frac{R}{100}\right)}^n \\ \Rightarrow 68921=64000{\left(1+\frac{2.5}{100}\right)}^n \\ \Rightarrow \frac{68921}{64000}={\left(1+\frac{25}{1000}\right)}^n \\ \Rightarrow \frac{68921}{64000}={\left(1+\frac{1}{40}\right)}^n \\ \Rightarrow \frac{68921}{64000}={\left(\frac{41}{40}\right)}^n \\ \Rightarrow {\left(\frac{41}{40}\right)}^3={\left(\frac{41}{40}\right)}^n \\ comparingtheexponentsasthebaseissame \\ \Rightarrow \boxed{n=3} \end{gathered}$$

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