Question

Find the amount and the compound interest.

No.	Principal (₹)	Rate (p.c.p.a.)	Duration (Years)
1	2000	5	2
2	5000	8	3
3	4000	7.5	2

Answer 1

(1) Here, P = ₹ 2000; R = 5 % ; N = 2 years

$$\begin{gathered} \mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{N}} \\ =2000{\left(1+\frac{5}{100}\right)}^2 \\ =2000{\left(\frac{105}{100}\right)}^2 \\ =2000{\left(\frac{21}{20}\right)}^2 \\ =2205\mathrm{Rupees} \\ \therefore \mathrm{Compound}\mathrm{Interest}\mathrm{after}2\mathrm{years}, \\ \mathrm{I}=\mathrm{Amount}-\mathrm{Principal} \\ =2205-2000 \\ =205\mathrm{Rupees} \end{gathered}$$
Hence, Amount = ₹ 2205 and Compound interest = ₹ 205.


(2) Here, P = ₹ 5000; R = 8 % ; N = 3 years

$$\begin{gathered} \mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{N}} \\ =5000{\left(1+\frac{8}{100}\right)}^3 \\ =5000{\left(\frac{108}{100}\right)}^3 \\ =5000{\left(\frac{27}{25}\right)}^3 \\ =6298.56\mathrm{Rupees} \\ \therefore \mathrm{Compound}\mathrm{Interest}\mathrm{after}3\mathrm{years}, \\ \mathrm{I}=\mathrm{Amount}-\mathrm{Principal} \\ =6298.56-5000 \\ =1298.56\mathrm{Rupees} \end{gathered}$$
Hence, Amount = ₹ 6298.56 and Compound interest = ₹ 1298.56


(3) Here, P = ₹ 4000; R = 7.5 % ; N = 2 years

$$\begin{gathered} \mathrm{A}=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{N}} \\ =4000{\left(1+\frac{7.5}{100}\right)}^2 \\ =4000{\left(1+\frac{75}{1000}\right)}^2 \\ =4000{\left(\frac{1075}{1000}\right)}^2 \\ =4000{\left(\frac{43}{40}\right)}^2 \\ =4622.50\mathrm{Rupees} \\ \therefore \mathrm{Compound}\mathrm{Interest}\mathrm{after}2\mathrm{years}, \\ \mathrm{I}=\mathrm{Amount}-\mathrm{Principal} \\ =4622.50-4000 \\ =622.50\mathrm{Rupees} \end{gathered}$$
Hence, Amount = ₹ 4622.50 and Compound interest = ₹ 622.50