Question

Shubhalaxmi took a loan of Rs 18000 from surya Finance to purchase a TV set. If the company charges compound interest at 12% per annum during the first year and $12\frac{1}{2}\%$ per annum during the second year, how much will she have to pay after 2 years?

Answer 1

$$\begin{gathered} \mathrm{Principal}\mathrm{amount},P\mathit{}=\mathrm{Rs}.18000 \\ \mathrm{Rate}\mathrm{of}\mathrm{interest}\mathrm{for}\mathrm{the}\mathrm{first}\mathrm{year},p=12\%\mathrm{p}.\mathrm{a}. \\ \mathrm{Rate}\mathrm{of}\mathrm{interest}\mathrm{for}\mathrm{the}\mathrm{second}\mathrm{year},q=12\frac{1}{2}\%\mathrm{p}.\mathrm{a}. \\ \mathrm{Time},\mathit{}n=2\mathrm{years} \\ \mathrm{The}\mathrm{formula}\mathrm{for}the\mathrm{amount}\mathrm{including}\mathrm{the}\mathrm{compound}\mathrm{interest}\mathrm{for}\mathrm{the}\mathrm{first}\mathrm{year}\mathrm{is}givenbelow: \\ A=\left\{P\times \left(1+\frac{p}{100}\right)\times \left(1+\frac{q}{100}\right)\right\} \\ =\mathrm{Rs}.\left\{18000\times \left(1+\frac{12}{100}\right)\times \left(1+\frac{25}{100\times 2}\right)\right\} \\ =\mathrm{Rs}.\left\{18000\times \left({\displaystyle \frac{100+12}{100}}\right)\times \left({\displaystyle 1+\frac{25}{200}}\right)\right\} \\ =\mathrm{Rs}.\left\{18000\times \left({\displaystyle \frac{100+12}{100}}\right)\times \left({\displaystyle 1+\frac{1}{8}}\right)\right\} \\ =\mathrm{Rs}.\left\{18000\times \left({\displaystyle \frac{100+12}{100}}\right)\times \left({\displaystyle \frac{8+1}{8}}\right)\right\} \\ =\mathrm{Rs}.\left\{18000\times \left({\displaystyle \frac{112}{100}}\right)\times \left({\displaystyle \frac{9}{8}}\right)\right\} \\ =\mathrm{Rs}.\left\{18000\times \left(1.12\right)\times \left(1.125\right)\right\} \\ =\mathrm{Rs}.22680 \\ \therefore \mathrm{Shubhalaxmi}\mathrm{has}\mathrm{to}\mathrm{pay}\mathrm{Rs}22680\mathrm{to}\mathrm{the}\mathrm{finance}\mathrm{company}\mathrm{after}2\mathrm{years}. \end{gathered}$$