Question

Use the formula to find the amount and the compound interest.

Example	Principal (Rs)	Rate (p.c.p.a)	Time (years)
(1)	8,000	10	2
(2)	6,400	12.5	2
(3)	10,000	10	2
(4)	15,000	10	3
(5)	20,000	05	3
(6)	16,000	$12\frac{1}{2}$	3

Answer 1

(1) Principal = Rs 8,000
Rate of interest = 10% p.a.
Number of years (N) = 2 years
Amount = $\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{N}}$
$$\begin{gathered} =8000{\left(1+\frac{10}{100}\right)}^2 \\ =8000{\left(1+\frac{1}{10}\right)}^2 \\ =8000{\left(\frac{10+1}{10}\right)}^2 \\ =8000{\left(\frac{11}{10}\right)}^2 \\ =\frac{8000\times 11\times 11}{10\times 10} \\ =\mathrm{Rs}9680 \end{gathered}$$
The amount is Rs 9680.
Compound Interest = Amount – Principal = 9680 – 8000 = Rs 1680
∴ Compound Interest = Rs 1680

(2) Principal = Rs 6,400
Rate of interest = 12.5% p.a.
Number of years (N) = 2 years
Amount $=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{N}}$
$$\begin{gathered} =6400{\left(1+\frac{12.5}{100}\right)}^2 \\ =6400{\left(1+\frac{125}{1000}\right)}^2 \\ =6400{\left(1+\frac{1}{8}\right)}^2 \\ =6400{\left(\frac{8+1}{8}\right)}^2 \\ =6400{\left(\frac{9}{8}\right)}^2 \\ =6400\times \frac{9}{8}\times \frac{9}{8} \\ =\mathrm{Rs}8100 \end{gathered}$$
The amount is Rs 8100.
Compound Interest = Amount – Principal = 8100 – 6400 = Rs 1700
∴ Compound Interest = Rs 1700

(3) Principal = Rs 10,000
Rate of interest = 10% p.a.
Number of Years (N) = 2 years
Amount $=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{N}}$
$$\begin{gathered} =10000{\left(1+\frac{10}{100}\right)}^2 \\ =10000{\left(1+\frac{1}{10}\right)}^2 \\ =10000{\left(\frac{11}{10}\right)}^2 \\ =\frac{10000\times 11\times 11}{10\times 10} \\ =\mathrm{Rs}12100 \end{gathered}$$
The amount is Rs 12100.
Compound Interest = Amount – Principal = 12100 – 10,000 = Rs 2100
∴ Compound Interest = Rs 2100

(4) Principal = Rs 15,000
Rate of interest = 10% p.a.
Number of years (N) = 3 years
Amount $=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{N}}$
$$\begin{gathered} =15000{\left(1+\frac{10}{100}\right)}^3 \\ =15000{\left(1+\frac{1}{10}\right)}^3 \\ =15000{\left(\frac{11}{10}\right)}^3 \\ =15000\times \frac{11}{10}\times \frac{11}{10}\times \frac{11}{10} \\ =\mathrm{Rs}19965 \end{gathered}$$

The amount is Rs 19965.
Compound Interest = Amount – Principal = 19965 – 15000 = Rs 4965
∴ Compound Interest = Rs 4965

(5) Principal = Rs 20,000
Rate of interest = 5% p.a.
Number of years (N) = 3 years
Amount $=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{N}}$
$$\begin{gathered} =20000{\left(1+\frac{5}{100}\right)}^3 \\ =20000{\left(1+\frac{1}{20}\right)}^3 \\ =20000{\left(\frac{21}{20}\right)}^3 \\ =20000\times \frac{21}{20}\times \frac{21}{20}\times \frac{21}{20} \\ =\mathrm{Rs}23152.50 \end{gathered}$$

The amount is Rs 23152.50 .
Compound Interest = Amount – Principal = 23152.50 – 20000 = Rs 3152.50
∴ Compound Interest = Rs 3152.50

(6) Principal = Rs 16,000
Rate of interest = $12\frac{1}{2}\%\mathrm{p}.\mathrm{a}.$ = 12.5% p.a.
Number of years (N) = 3 years
Amount $=\mathrm{P}{\left(1+\frac{\mathrm{R}}{100}\right)}^{\mathrm{N}}$
$$\begin{gathered} =16000{\left(1+\frac{12.5}{100}\right)}^3 \\ =16000{\left(1+\frac{125}{1000}\right)}^3 \\ =16000{\left(1+\frac{1}{8}\right)}^3 \\ =16000{\left(\frac{9}{8}\right)}^3 \\ =16000\times \frac{9}{8}\times \frac{9}{8}\times \frac{9}{8} \\ =\mathrm{Rs}22781.25 \end{gathered}$$
The amount is Rs 22781.25 .
Compound Interest = Amount – Principal = 22781.25 – 16000 = Rs 6781.25
∴ Compound Interest = Rs 6781.25