Question

Compound interest on certain sum of money at 5 % per annum for 2 years is rupees to 246 what will be the simple interest on the same sum for 3 years at 6 % per annum find difference between compound interest and simple interest on same principal for 3 years at 6 % per annum

Answer 1

$$\begin{gathered} \mathrm{Using}, \\ \mathrm{C}.\mathrm{I}=\mathrm{P}\left[\right(1+\frac{\mathrm{r}}{100}{)}^{\mathrm{n}}-1] \\ 246=\mathrm{P}[1+\frac{5}{100}{)}^2-1] \\ 246=\mathrm{P}[(\frac{21}{20}{)}^2-1] \\ 246=\mathrm{P}\left[\frac{441-400}{400}\right] \\ 246=\mathrm{P}\times \frac{41}{400} \\ \mathrm{P}=\frac{246\times 400}{41}=\mathrm{Rs}2400 \\ \mathrm{Now}, \\ \mathrm{P}=\mathrm{Rs}2400,\mathrm{r}=6\%,\mathrm{t}=3\mathrm{years} \\ \mathrm{S}.\mathrm{I}=\frac{\mathrm{P}\times \mathrm{r}\times \mathrm{t}}{100}=\frac{2400\times 6\times 3}{100}=\mathrm{Rs}432 \\ \mathrm{Also},\mathrm{C}.\mathrm{I}\mathrm{for}\mathrm{P}=\mathrm{Rs}2400,\mathrm{r}=6\%\mathrm{and}\mathrm{t}=3\mathrm{years} \\ \mathrm{C}.\mathrm{I}==\mathrm{P}\left[\right(1+\frac{\mathrm{r}}{100}{)}^{\mathrm{n}}-1] \\ \mathrm{C}.\mathrm{I}==2400[(1+\frac{6}{100}{)}^3-1] \\ \mathrm{C}.\mathrm{I}=2400\left[\right(1.06{)}^3-1]=\mathrm{Rs}458.44 \\ \mathrm{Reqd}\mathrm{Difference}=\mathrm{C}.\mathrm{I}-\mathrm{S}.\mathrm{I}=\mathrm{Rs}458.44-\mathrm{Rs}432=\mathrm{Rs}23.44 \end{gathered}$$