Answer

Verified

417.6k+ views

**Hint:**We know that the amount formula for the compound interest is given as

$A = P{\left[ {1 + \dfrac{R}{n}} \right]^{nT}}$

Here $n = 2$ as the interest is compounded semi-annually and the rate is $12\% $ per annum and we need to find it for $1\dfrac{1}{2}{\text{ years}}$. So $T = 1\dfrac{1}{2}{\text{ years}}$

And $P$ is given as ${\text{Rs12000}}$

Put it in the formula we will get the answer.

**Complete step-by-step answer:**

Here we are given on ${\text{Rs12000}}$ for $1\dfrac{1}{2}{\text{ years}}$ at the rate of $12\% $ per annum, the interest is compounded semi-annually and we need to compute the compound interest.

So as we know that compound interest is addition of the interest to the principle sum of the loan or deposit and here we are given $P$ as ${\text{Rs12000}}$

Let us take an example where $P$ amount is invested at annual rate of $R$compounded $n$ times.

So the value of the investment after $T$ years will be $A = P{\left[ {1 + \dfrac{R}{n}} \right]^{nT}}$

Here A is the future amount of the investment and P is the principle investment value and R is the annual interest rate and n is the number of times that interest is compounded per unit t

T is the time the money is invested.

So we are given that

$P = {\text{Rs12000}}$, $R = 12\% $, $T = 1\dfrac{1}{2}{\text{ years}}$

So we will get

$A = P{\left[ {1 + \dfrac{R}{n}} \right]^{nT}}$

$A = 12000{\left[ {1 + \dfrac{{12}}{2}} \right]^{2\left( {\dfrac{3}{2}} \right)}}$

On simplifying, we get that $A = 12000{\left( {1 + 6} \right)^3}$

$A = 12000{(7)^3} = {\text{Rs 4116000}}$

Therefore compound interest$ = $amount $ - $ principal $

= 4116000 - 12000 \\

= {\text{Rs 4104000}} \\

$

**So after $1.5{\text{ years}}$ he got ${\text{Rs 4104000}}$ as compound interest.**

**Note:**Simple interest is simply given by the formula $SI = \dfrac{{(P)(R)(T)}}{{100}}$ and amount is given by $A = P + SI$

And in case of compound interest amount is given by

$A = P{\left[ {1 + \dfrac{R}{n}} \right]^{nT}}$

Compound interest is given by $ = A - P$

Where A is the amount and P is the principle amount.

Recently Updated Pages

List the name of the women who had achieved literacy class 8 social science CBSE

Select the antonym for the word EXTREME from the below class 8 english CBSE

Which of the following was not an important crop of class 8 social science CBSE

Which temples were built by the Nayaks of Madurai This class 8 social science CBSE

Choose the word which can be substituted for the given class 8 english CBSE

Choose the correct option whose meaning is given below class 8 english CBSE

Trending doubts

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which are the Top 10 Largest Countries of the World?

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE

Difference Between Plant Cell and Animal Cell

10 examples of law on inertia in our daily life