Question

Compute the amount and the compound interest in each of the following by using the formulae when:
(i) Principal = Rs 3000, Rate = 5%, Time = 2 years
(ii) Principal = Rs 3000, Rate = 18%, Time = 2 years
(iii) Principal = Rs 5000, Rate = 10 paise per rupee per annum, Time = 2 years
(iv) Principal = Rs 2000, Rate = 4 paise per rupee per annum, Time = 3 years
(v) Principal = Rs 12800, Rate = $7\frac{1}{2}\%$, Time = 3 years
(vi) Principal = Rs 10000, Rate 20% per annum compounded half-yearly, Time = 2 years
(vii) Principal = Rs 160000, Rate = 10 paise per rupee per annum compounded half-yearly, Time = 2 years.

Answer 1

$$\begin{gathered} \mathrm{Applying}\mathrm{the}\mathrm{rule}\mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{n}}\mathrm{on}\mathrm{the}\mathrm{given}\mathrm{situations},\mathrm{we}\mathrm{get}: \\ \left(\mathrm{i}\right) \\ \mathrm{A}=3,000{\left(1+\frac{5}{100}\right)}^2 \\ =3,000{\left(1.05\right)}^2 \\ =\mathrm{Rs}3,307.50 \\ \mathrm{Now}, \\ \mathrm{CI}=\mathrm{A}-\mathrm{P} \\ =\mathrm{Rs}3,307.50-\mathrm{Rs}3,000 \\ =\mathrm{Rs}307.50 \\ \left(\mathrm{ii}\right) \\ \mathrm{A}=3,000{\left(1+\frac{18}{100}\right)}^2 \\ =3,000{\left(1.18\right)}^2 \\ =\mathrm{Rs}4,177.20 \\ \mathrm{Now}, \\ \mathrm{CI}=\mathrm{A}-\mathrm{P} \\ =\mathrm{Rs}4,177.20-\mathrm{Rs}3,000 \\ =\mathrm{Rs}1,177.20 \\ \left(\mathrm{iii}\right) \\ \mathrm{A}=5,000{\left(1+\frac{10}{100}\right)}^2 \\ =5,000{\left(1.10\right)}^2 \\ =\mathrm{Rs}6,050 \\ \mathrm{Now}, \\ \mathrm{CI}=\mathrm{A}-\mathrm{P} \\ =\mathrm{Rs}6,050-\mathrm{Rs}5,000 \\ =\mathrm{Rs}1,050 \\ \left(\mathrm{iv}\right) \\ \mathrm{A}=2,000{\left(1+\frac{4}{100}\right)}^3 \\ =2,000{\left(1.04\right)}^3 \\ =\mathrm{Rs}2,249.68 \\ \mathrm{Now}, \\ \mathrm{CI}=\mathrm{A}-\mathrm{P} \\ =\mathrm{Rs}2,249.68-\mathrm{Rs}2,000 \\ =\mathrm{Rs}249.68 \\ \left(\mathrm{v}\right) \\ \mathrm{A}=12,800{\left(1+\frac{7.5}{100}\right)}^3 \\ =12,800{\left(1.075\right)}^3 \\ =\mathrm{Rs}15,901.40 \\ \mathrm{Now}, \\ \mathrm{CI}=\mathrm{A}-\mathrm{P} \\ =\mathrm{Rs}15,901.40-\mathrm{Rs}12,800 \\ =\mathrm{Rs}3,101.40 \\ \left(\mathrm{vi}\right) \\ \mathrm{A}=10,000{\left(1+\frac{20}{200}\right)}^4 \\ =10,000{\left(1.1\right)}^4 \\ =\mathrm{Rs}14,641 \\ \mathrm{Now}, \\ \mathrm{CI}=\mathrm{A}-\mathrm{P} \\ =\mathrm{Rs}14,641-\mathrm{Rs}10,000 \\ =\mathrm{Rs}4,641 \\ \left(\mathrm{vii}\right) \\ \mathrm{A}=16,000{\left(1+\frac{10}{200}\right)}^4 \\ =16,000{\left(1.05\right)}^4 \\ =\mathrm{Rs}19,448.1 \\ \mathrm{Now}, \\ \mathrm{CI}=\mathrm{A}-\mathrm{P} \\ =\mathrm{Rs}19,448.1-\mathrm{Rs}16,000 \\ =\mathrm{Rs}3,448.1 \end{gathered}$$