Question

Q. Find the compound interest on Rs. 2000 for 1 year at 5% per annum, interest being compounded
half-yearly. Also calculate the interest if it was compounded annually. Which is more and by how much?

Answer 1

$$\begin{gathered} \mathrm{Principal},\mathrm{P}=\mathrm{Rs}2000 \\ \mathrm{Rate},\mathrm{R}=5\%\mathrm{p}.\mathrm{a}.=\frac{5}{2}\%\mathrm{per}\mathrm{half}\mathrm{year} \\ \mathrm{Time},\mathrm{n}=1\mathrm{yr}=2\mathrm{half}\mathrm{yrs} \\ \mathrm{Amount},\mathrm{A}=\mathrm{P}{\left[1+\frac{\mathrm{R}}{100}\right]}^{\mathrm{n}} \\ =2000{\left[1+\frac{5}{200}\right]}^2 \\ =2000\times \frac{41}{40}\times \frac{41}{40} \\ =\mathrm{Rs}2101.25 \\ \mathrm{CI}=\mathrm{A}-\mathrm{P}=2101.25-2000=\mathrm{Rs}101.25 \\ \mathrm{Principal},\mathrm{P}=\mathrm{Rs}2000 \\ \mathrm{Rate},\mathrm{R}=5\%\mathrm{p}.\mathrm{a}. \\ \mathrm{Time},\mathrm{n}=1\mathrm{yr} \\ \mathrm{Amount},\mathrm{A}=\mathrm{P}{\left[1+\frac{\mathrm{R}}{100}\right]}^{\mathrm{n}} \\ =2000{\left[1+\frac{5}{100}\right]}^1 \\ =2000\times \frac{41}{40} \\ =\mathrm{Rs}2050 \\ \mathrm{CI}=\mathrm{A}-\mathrm{P}=2050-2000=\mathrm{Rs}50 \\ \mathrm{So},\mathrm{interest}\mathrm{compounded}\mathrm{half}\mathrm{yearly}\mathrm{is}\mathrm{more}\mathrm{than}\mathrm{interest}\mathrm{compounded}\mathrm{semi}\mathrm{annually}. \\ \mathrm{Difference}=101.25-50=\mathrm{Rs}51.25 \end{gathered}$$