Question

21) Which investment is better and by how much?
(i) Rs 12000 at 6 % p.a simple interest for 2 years.
(ii) Rs. 12000 at 6 % p.a. compound interest for 2 years.
(Answer : Second is better by Rs 43.20)

Answer 1

Dear student,
Here is the solution of your asked query:
$$\begin{gathered} \left(\mathrm{i}\right)\mathrm{Here},\mathrm{P}=\mathrm{Rs}.12000 \\ \mathrm{R}=6\%\mathrm{p}.\mathrm{a}. \\ \mathrm{T}=2\mathrm{years} \\ \mathrm{So},\mathrm{simple}\mathrm{interest}=\frac{\mathrm{P}\times \mathrm{R}\times \mathrm{T}}{100}=\frac{12000\times 6\times 2}{100}=\mathrm{Rs}.1440 \\ \mathrm{So},\mathrm{total}\mathrm{amount}\mathrm{after}2\mathrm{years}=\mathrm{Rs}.12000+\mathrm{Rs}.1440=\mathrm{Rs}.13440 \\ \left(\mathrm{ii}\right)\mathrm{Here},\mathrm{P}=\mathrm{Rs}.12000 \\ \mathrm{R}=6\%\mathrm{p}.\mathrm{a}. \\ \mathrm{T}=2\mathrm{years} \\ \mathrm{so},\mathrm{amount}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{T}} \\ =12000{\left(1+\frac{6}{100}\right)}^2 \\ =12000\times {\left(\frac{53}{50}\right)}^2 \\ =12000\times \frac{53}{50}\times \frac{53}{50} \\ =13483.2 \\ \mathrm{So},\mathrm{the}\mathrm{total}\mathrm{amount}\mathrm{after}2\mathrm{years}=\mathrm{Rs}.13483.2 \\ \mathrm{Therefore},\mathrm{investement}\mathrm{is}\mathrm{better}\mathrm{in}\left(\mathrm{ii}\right)\mathrm{by}\left(\mathrm{Rs}.13483.2-\mathrm{Rs}.13440\right)\mathrm{i}.\mathrm{e}.\mathrm{Rs}.43.20 \end{gathered}$$
Regards