Question

A person invests ₹10000 for two years at a certain rate of interest, compounded annually. At the end of one year this sum amounts to ₹11200. Calculate:-
i) The rate of interest.
ii) The amount at the end of second year.

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Step-by-step explanation:

$\bf{\underline{\underline\red{Given:-}}}$

• Amount invested by the person = ₹10000

• Time = 2 years.

• At the end of 1 year the sum amounts to ₹11200

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The rate of interest.

• The amount at the end of second year.

$\bf{\underline{\underline\green{Solution:-}}}$

As we know that:-

The amount is given by the formula:-

$\boxed{ \rm \leadsto Amount \: = P{ \bigg(1 + \frac{r}{100} \bigg) }^{t} }$

Here:-

• Amount = ₹11200

• P = principal = ₹10000

• r = rate of interest

• t = time = 1 year

Substituting the values:-

$\rm \longrightarrow 11200\: = 10000 { \bigg(1 + \dfrac{r}{100} \bigg) }^{1}$

$\rm \longrightarrow 11200\: = 10000 \bigg(1 + \dfrac{r}{100} \bigg)$

$\rm \longrightarrow \dfrac{11200}{10000}\: = \bigg(1 + \dfrac{r}{100} \bigg)$

$\rm \longrightarrow \dfrac{112}{100}\: = 1 + \dfrac{r}{100}$

$\rm \longrightarrow \dfrac{112}{100}\: - 1 = \dfrac{r}{100}$

$\rm \longrightarrow \dfrac{112 - 100}{100}\: = \dfrac{r}{100}$

$\rm \longrightarrow \dfrac{12 }{100}\: = \dfrac{r}{100}$

$\rm \longrightarrow \dfrac{12 }{100}\: \times 100 = {r}$

$\rm \longrightarrow r = 12\%$

Amount after 2 years.

• P = principal = ₹10000

• r = rate of interest = 12%

• t = time = 2 years

Substituting the values.

$\rm \longrightarrow 10000 { \bigg(1 + \dfrac{12}{100} \bigg) }^{2}$

$\rm \longrightarrow 10000 { \bigg(1 + \dfrac{3}{25} \bigg) }^{2}$

$\rm \longrightarrow 10000 { \bigg( \dfrac{28}{25} \bigg) }^{2}$

$\rm \longrightarrow \dfrac{10000 \times 28 \times 28}{25 \times 25}$

$\rm \longrightarrow 16 \times 28 \times 28$

$\rm \longrightarrow 12544$

Therefore:-

$\boxed{\rm \pink{ Rate \: of \: interest \: = 12\%} }$

$\boxed{\rm \purple{ Amount \: at \: the \: end \: of \: 2 \: years = Rs.12544} }$