Question

a sum of rupees 1000 is invested at 4% per annum at simple interest. calculate the interest at the end of each year. show that these interest form an AP using this find the interest at the end of 20 years

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{know}\mathrm{that}: \\ \mathrm{simple}\mathrm{interest}=\frac{\mathrm{Principal}\times \mathrm{rate}\times \mathrm{time}}{100} \\ \mathrm{Interest}\mathrm{at}\mathrm{the}\mathrm{end}\mathrm{of}\mathrm{first}\mathrm{year}=\frac{1000\times 4\times 1}{100}=\mathrm{Rs}40 \\ \mathrm{Interest}\mathrm{at}\mathrm{the}\mathrm{end}\mathrm{of}\mathrm{second}\mathrm{year}=\frac{1000\times 4\times 2}{100}=\mathrm{Rs}80 \\ \mathrm{Interest}\mathrm{at}\mathrm{the}\mathrm{end}\mathrm{of}\mathrm{third}\mathrm{year}=\frac{1000\times 4\times 3}{100}=\mathrm{Rs}120 \\ \mathrm{and}\mathrm{so}\mathrm{on}. \\ \mathrm{Now},\mathrm{the}\mathrm{list}\mathrm{of}\mathrm{interest}\left(\mathrm{in}\mathrm{Rs}\right)\mathrm{in}\mathrm{each}\mathrm{year}\mathrm{is}: \\ 40,80,120,........ \\ \mathrm{The}\mathrm{above}\mathrm{list}\mathrm{is}\mathrm{in}\mathrm{AP}\mathrm{with}\mathrm{first}\mathrm{term},\mathrm{a}=40\mathrm{and}\mathrm{common}\mathrm{difference},\mathrm{d}=80-40=40 \\ \mathrm{Interest}\mathrm{at}\mathrm{the}\mathrm{end}\mathrm{of}20\mathrm{yrs}={\mathrm{t}}_{20}=\mathrm{a}+19\mathrm{d}=40+19\times 40=40+760=\mathrm{Rs}800 \end{gathered}$$