Question

Write the proper numbers in the blanks in the table below.

Ex.	Principal (Rs)	Rate (p.c.p.a)	Time (years)	Simple Interest	Compound Interest	Difference
(1)	3,000	5	2	........	........	........
(2)	1,000	10	2	........	........	........
(3)	25,000	12	3	........	........	........
(4)	64,000	$12\frac{1}{2}$	3	........	........	........
(5)	20,000	10.5	2	........	........	........

Answer 1

(1) Principal = Rs 3,000
Rate of interest = 5% p.a.
Number of years (N) = 2 years
Simple Interest$=\frac{\mathrm{Principal}\times \mathrm{Rate}\times \mathrm{Time}}{100}=\frac{3000\times 5\times 2}{100}=\mathrm{Rs}300$
Amount for Compound Interest$=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{N}}$
$$\begin{gathered} =3000{\left(1+\frac{5}{100}\right)}^2 \\ =3000{\left(1+\frac{1}{20}\right)}^2 \\ =3000{\left(\frac{21}{20}\right)}^2 \\ =3000\times \frac{21}{20}\times \frac{21}{20} \\ =\mathrm{Rs}3307.50 \end{gathered}$$

The amount is Rs 3307.50.
Compound Interest = Amount − Principal =3307.5 − 3000 = Rs 307.50
∴ Compound Interest = Rs 307.50
Difference between Compound Interest and Simple Interest= Compound Interest − Simple Interest
= Rs 307.50 − Rs 300 = Rs 7.50
∴ Simple Interest = Rs 300
Compound Interest = Rs 307.50
Difference between Compound Interest and Simple Interest= Rs 7.50

(2) Principal = Rs 1,000
Rate of interest = 10% p.a.
Number of years(N) = 2 years
Simple Interest$=\frac{\mathrm{Princiapl}\times \mathrm{Rate}\times \mathrm{Time}}{100}=\frac{1000\times 10\times 2}{100}=\mathrm{Rs}200$
Amount for Compound Interest$=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{N}}$
$$\begin{gathered} =1000{\left(1+\frac{10}{100}\right)}^2 \\ =1000{\left(1+\frac{1}{10}\right)}^2 \\ =1000{\left(\frac{11}{10}\right)}^2 \\ =1000\times \frac{11}{10}\times \frac{11}{10} \\ =\mathrm{Rs}1210 \end{gathered}$$

The amount is Rs 1210.
Compound Interest = Amount − Principal = 1210 − 1000 = Rs 210
∴ Compound Interest = Rs 210
Difference between Compound Interest and Simple Interest = Compound Interest − Simple Interest
= Rs 210 − Rs 200 = Rs 10
∴ Simple Interest = Rs 200
Compound Interest = Rs 210
Difference between Compound Interest and Simple Interest = Rs 10

(3) Principal = Rs 25,000
Rate of interest = 12% p.a.
Number of years (N) = 3 years
Simple Interest = $\frac{\mathrm{Principal}\times \mathrm{Rate}\times \mathrm{Time}}{100}=\frac{25000\times 12\times 3}{100}=\mathrm{Rs}9000$
Amount for Compound Interest $=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{N}}$
$$\begin{gathered} =25000{\left(1+\frac{12}{100}\right)}^3 \\ =25000{\left(1+\frac{3}{25}\right)}^3 \\ =25000{\left(\frac{28}{25}\right)}^3 \\ =25000\times \frac{28}{25}\times \frac{28}{25}\times \frac{28}{25} \\ =\mathrm{Rs}35123.20 \end{gathered}$$

The amount is Rs 35123.20 .
Compound Interest = Amount − Principal
= 35123.20 − 25,000 = Rs 10,123.20
∴ The Compound Interest = Rs 10,123.20
Difference between Compound Interest and Simple Interest= Compound Interest − Simple Interest
= Rs 10,123.20 − Rs 9000 = Rs 1123.20
∴ Simple Interest= Rs 9000
Compound Interest= Rs 10,123.20
Difference between Compound Interest and Simple Interest = Rs 1123.20

(4) Principal =Rs 64,000
Rate of interest = $12\frac{1}{2}\%\mathrm{p}.\mathrm{a}.$ = 12.5% p.a.
Number of years (N) = 3 years
Simple Interest$=\frac{\mathrm{Principal}\times \mathrm{Rate}\times \mathrm{Time}}{100}=\frac{64000\times 12.5\times 3}{100}=\mathrm{Rs}24000$
Amount for Compound Interest$=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{N}}$
$$\begin{gathered} =64000{\left(1+\frac{12.5}{100}\right)}^3 \\ =64000{\left(1+\frac{125}{1000}\right)}^3 \\ =64000{\left(1+\frac{1}{8}\right)}^3 \\ =64000{\left(\frac{9}{8}\right)}^3 \\ =64000\times \frac{9}{8}\times \frac{9}{8}\times \frac{9}{8} \\ =\mathrm{Rs}91125 \end{gathered}$$

The amount is Rs 91125.
Compound Interest = Amount − Principal = 91125 − 64,000 = Rs 27,125
∴ Compound Interest = Rs 27,125
Difference between Compound Interest and Simple Interest= Compound Interest − Simple Interest
= Rs 27,125 − Rs 24000 = Rs 3,125
∴ Simple Interest= Rs 24000
Compound Interest = Rs 27,125
Difference between Compound Interest and Simple Interest = Rs 3,125

(5) Principal =Rs 20,000
Rate of interest= 10.5% p.a.
Number of years (N) = 2 years
Simple Interest $=\frac{\mathrm{Principal}\times \mathrm{Rate}\times \mathrm{Time}}{100}=\frac{20000\times 10.5\times 2}{100}=\mathrm{Rs}4200$
Amount for Compound Interest$=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{N}}$
$$\begin{gathered} =20000{\left(1+\frac{10.5}{100}\right)}^2 \\ =20000{\left(1+\frac{105}{1000}\right)}^2 \\ =20000{\left(1+\frac{21}{200}\right)}^2 \\ =20000{\left(\frac{221}{200}\right)}^2 \\ =20000\times \frac{221}{200}\times \frac{221}{200} \\ =\mathrm{Rs}24420.50 \end{gathered}$$
The amount is Rs 24420.50 .
Compound Interest = Amount − Principal = 24420.50 − 20,000 = Rs 4420.50
∴ Compound Interest = Rs 4420.50
Difference between Compound Interest and Simple Interest= Compound Interest − Simple Interest
= Rs 4420.50 − Rs 4200 = Rs 220.50
∴ Simple Interest= Rs 4200
Compound Interest= Rs 4420.50
Difference between Compound Interest and Simple Interest = Rs 220.50