Question

Find the rate percent per annum if rs 2000 amount to rs 2662 in 1½ years interest being compounded half yearly​

Answer 1

Step-by-step explanation:

Given:-

• Principal = Rs.2000

• Amount = Rs.2662

• Time = 1 ½ years

• Interest compounded half-yearly.

To Find:-

• The rate of interest.

Solution:-

Time = 1 ½ years = 3 half years

The formula for finding Amount is:-

$\leadsto \sf Amount = P \bigg(1 + \dfrac{r}{100}\bigg)^n$

Here:-

• A = Amount = Rs.2662

• P = Principal = Rs.2000

• r = rate = ?

• n = time = 3 half years

Substituting the values:-

$\implies \sf2662= 2000 \times \bigg(1 + \dfrac{r}{100}\bigg)^3$

$\implies \sf \dfrac{2662}{2000} = \bigg(1 + \dfrac{r}{100}\bigg)^3$

$\implies \sf 1.331 = \bigg(1 + \dfrac{r}{100}\bigg)^3$

$\implies \sf {(1.1)}^{3} = \bigg(1 + \dfrac{r}{100}\bigg)^3$

$\implies \sf 1.1= 1 + \dfrac{r}{100}$

$\implies \sf \dfrac{r}{100} = 1.1 - 1$

$\implies \sf \dfrac{r}{100} = 0.1$

$\implies \sf r = 0.1 \times 100$

$\implies \sf r = 10$

For half- yearly, Rate = 10%

Rate% per annum = 20%

$\large \underline{ \boxed{\sf \therefore \: \textsf{ \textbf{Rate \: of \: Interest = 20\%}}}}$

Answer 2

Given:-

• Principal (p) = Rs.2000
• Amount (A) = Rs.2662
• Time (n) = 1 ½ years = 3 half years

Find:-

• Rate percent per Annum

Solution:-

Let take rate percent as R ( per half year)

By using the formula⤵

${ \boxed{ \rm{A = P {(1 + \frac{R}{100}) }^{n} }}}$

${ \to{ \rm{2663 = 2000 ( {1 + \frac{R}{100} )}^{3} }}}$

${ \to{ \rm{ {(1 + \frac{R}{100}) }^{3} = \frac{2663}{2000} }}}$

${ \to{ \rm{ {(1 + \frac{R}{100}) }^{3} = \frac{1331}{1000} }}}$

${ \to{ \rm{ {(1 + \frac{R}{100} )}^{3} = {( \frac{11}{10} )}^{3} }}}$

The powers will get cancelled

${ \to{ \rm{ \frac{100 + R}{100} = \frac{11}{10} }}}$

${ \to{ \rm{1000 + 10R = 1100}}}$

${ \to{ \rm{10R = 1100 - 1000}}}$

${ \to{ \rm{10R = 100}}}$

${ \to{ \rm{R = \frac{100}{10} = 10}}}$

${ \to{ \rm{R = 10}}}$

Rate percent per half year is 10%

Therefore,

Rate percent per Annum = 20%