If ruppe1000 was invested on 5% compound interest, compounded annually, when will the graph for the interest in one, two, three, four and five years be a linear graph?

$$\begin{gathered} \mathrm{Hi}, \\ \mathrm{We} \mathrm{know} \mathrm{that} \\ \mathrm{A} = \mathrm{P}{\left(1+\frac{\mathrm{r}}{100}\right)}^{\mathrm{t}} \\ \mathrm{for} \mathrm{one} \mathrm{year} \mathrm{t} =1 , \mathrm{r} = 5 \%, \\ \mathrm{A} = 1000\times \frac{105}{100}=1050 \\ \mathrm{so} \mathrm{interest} = \mathrm{A} - \mathrm{P} = \mathrm{Rs}. 50 \\ \mathrm{For} \mathrm{two} \mathrm{year} \\ \mathrm{A} = \mathrm{P}{\left(1+\frac{\mathrm{r}}{100}\right)}^{\mathrm{t}} \\ \mathrm{for} \mathrm{two} \mathrm{year} \mathrm{t} =2 , \mathrm{r} = 5 \%, \\ \mathrm{A} = 1000\times {\left(1+\frac{5}{100}\right)}^2=1000\times \frac{105}{100}\times \frac{105}{100}=1102.5 \\ \mathrm{so} \mathrm{interest} = \mathrm{A} - \mathrm{P} = \mathrm{Rs}. 102.5 \\ \mathrm{For} \mathrm{three} \mathrm{year} \\ \mathrm{A} = \mathrm{P}{\left(1+\frac{\mathrm{r}}{100}\right)}^{\mathrm{t}} \\ \mathrm{for} \mathrm{three} \mathrm{year} \mathrm{t} =3 , \mathrm{r} = 5 \%, \\ \mathrm{A} = 1000\times {\left(1+\frac{5}{100}\right)}^3=1000\times \frac{105}{100}\times \frac{105}{100}\times \frac{105}{100}=1157.625 \\ \mathrm{so} \mathrm{interest} = \mathrm{A} - \mathrm{P} = \mathrm{Rs}. 157.625 \\ \mathrm{For} \mathrm{four} \mathrm{year} \\ \mathrm{A} = \mathrm{P}{\left(1+\frac{\mathrm{r}}{100}\right)}^{\mathrm{t}} \\ \mathrm{for} \mathrm{four} \mathrm{year} \mathrm{t} =4 , \mathrm{r} = 5 \%, \\ \mathrm{A} = 1000\times {\left(1+\frac{5}{100}\right)}^4=1000\times \frac{105}{100}\times \frac{105}{100}\times \frac{105}{100}\times \frac{105}{100}=1215.506 \\ \mathrm{so} \mathrm{interest} = \mathrm{A} - \mathrm{P} = \mathrm{Rs}. 215.506 \\ \mathrm{For} \mathrm{five} \mathrm{year} \\ \mathrm{A} = \mathrm{P}{\left(1+\frac{\mathrm{r}}{100}\right)}^{\mathrm{t}} \\ \mathrm{for} \mathrm{five} \mathrm{year} \mathrm{t} =5 , \mathrm{r} = 5 \%, \\ \mathrm{A} = 1000\times {\left(1+\frac{5}{100}\right)}^5=1000\times \frac{105}{100}\times \frac{105}{100}\times \frac{105}{100}\times \frac{105}{100}\times \frac{105}{100}=1276.282 \\ \mathrm{so} \mathrm{interest} = \mathrm{A} - \mathrm{P} = \mathrm{Rs}. 276.282 \\ \mathrm{Now} \mathrm{plotting} \mathrm{the} \mathrm{graph} \mathrm{for} \mathrm{these} \mathrm{years} \mathrm{and} \mathrm{inetrest} \end{gathered}$$



Now they will not be linear as though here they look like linear but they will not be their graph will be like hyperbola or quadratic graph. This is so because simple ineterest from linear relation but not compound interest