Answer

Verified

381.6k+ views

**Hint:**We have to find the value of compound interest. Already we know the formula of compound interest. Using the given values and using the formula and substitute the values in the formula. And simply find the value of compound interest.

Formula used:

\[A = P\left[ {\left( {1 + \dfrac{{{r_1}}}{{100}}} \right)\left( {1 + \dfrac{{{r_2}}}{{100}}} \right)} \right]\];

Here,

$A = $ Amount;

$P = $ Principle amount;

$r = $Rate of interest per year;

$C.I = amount - principle$

**Complete step-by-step solution:**

In this problem we have to find the value of compound interest.

In this problem the given values are,

Principal amount is six thousand.

Rate of interests are five percent and ten percent.

$P = 6000$

\[{r_1} = 5\% \]

\[{r_2} = 10\% \]

We know that the formula,

\[A = P\left[ {\left( {1 + \dfrac{{{r_1}}}{{100}}} \right)\left( {1 + \dfrac{{{r_2}}}{{100}}} \right)} \right]\]

Substitute the values in the formula, we get,

$A = 6000\left[ {\left( {1 + \dfrac{5}{{100}}} \right)\left( {1 + \dfrac{{10}}{{100}}} \right)} \right]$

Cancel the common terms in the above equation,

Here, hundred is the multiplication of five and twenty and

Hundred is the multiplication of ten and ten.

Therefore, we have,

$ = 6000\left[ {\left( {1 + \dfrac{1}{{20}}} \right)\left( {1 + \dfrac{1}{{10}}} \right)} \right]$

Take Least common multiple inside the bracket,

Least common multiple for one and twenty is twenty and

Least common multiple for one and ten is ten.

Therefore we have,

$ = 6000\left[ {\left( {\dfrac{{20 + 1}}{{20}}} \right)\left( {\dfrac{{10 + 1}}{{10}}} \right)} \right]$

Add the values, we have,

$ = 6000\left[ {\left( {\dfrac{{21}}{{20}}} \right)\left( {\dfrac{{11}}{{10}}} \right)} \right]$

Simplify the values we have,

$ = 60\left[ {\left( {\dfrac{{21}}{2}} \right)\left( {\dfrac{{11}}{1}} \right)} \right]$

Now cancel the value sixty by two, we have

$ = 30\left[ {\left( {21} \right)\left( {11} \right)} \right]$

Now multiply the values, we have

$A = 6930$

Now we find the amount for the given problem,

Now we have to find the value of compound interest.

We know that the formula,

$C.I = amount - principle$

We already know the value of the principal amount and we find the amount value. Now substitute the values already we knows,

We get,

$C.I = 6930 - 6000$

Subtracting the values we get,

$ = 930$

Therefore the compound interest is,

$C.I = 930$

**Note:**Compound interest is an interest calculated on the principal amount which we have. This also includes all the accumulated interest. In mathematics, compound interest gives each and every time interest is paid onto the principal amount. In compound interest for every time we have to work a new calculation on it.

Recently Updated Pages

what is the correct chronological order of the following class 10 social science CBSE

Which of the following was not the actual cause for class 10 social science CBSE

Which of the following statements is not correct A class 10 social science CBSE

Which of the following leaders was not present in the class 10 social science CBSE

Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE

Which one of the following places is not covered by class 10 social science CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Who was the Governor general of India at the time of class 11 social science CBSE

How do you graph the function fx 4x class 9 maths CBSE

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE

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

Why is there a time difference of about 5 hours between class 10 social science CBSE

Difference Between Plant Cell and Animal Cell