Answer
Verified
413.4k+ views
Hint: In order to find out the value of compound interest after 5 years, we have to use the formula for compound interest mentioned below,
$A = P{\left( {1 + \dfrac{r}{100}} \right)^{nt}}$
Where, $A = $ final amount
$P = $ initial principal balance
$r = $ interest rate
$n = $ number of times interest applied per time period
$t = $ number of times period elapsed
Complete step-by-step answer:
In the first case we have 5 year time and an amount of 24000 and principal amount is 12000. So, by applying the above mentioned formula we will get,
24000 = 12000${\left( {1 + \dfrac{r}{{100}}} \right)^5}$
$
\Rightarrow \dfrac{{24000}}{{12000}} = {\left( {1 + \dfrac{r}{{100}}} \right)^5} \\
\Rightarrow 2 = {\left( {1 + \dfrac{r}{{100}}} \right)^5} \\
$
We have to find out the value of compound interest after 20 years. For that the value of exponent must be 20.
Multiply the exponent of both sides by 4
${2^4} = $ ${\left( {{{\left( {1 + \dfrac{r}{{100}}} \right)}^5}} \right)^4}$
16$ = {\left( {1 + \dfrac{r}{{100}}} \right)^{20}}$
Multiply P that is 12000 on both sides,
$16 \times 12000 = {\left( {1 + \dfrac{r}{{100}}} \right)^{20}} \times 12000$
We can see that here ${\left( {1 + \dfrac{r}{{100}}} \right)^{20}} \times 12000$ is the amount formula for 20 years.
So,
Amount $ = {\text{ 12000}}\left( {16} \right) = 192000$
After 20 years it will become Rs. 192000.
$\therefore $ Option B is correct.
Note: In this particular question, to find out the value of compound interest we have to use the general formula for compound interest. We can easily solve this question by deriving the amount formula like we did in the question. Also it is important to note that compound interest is different from simple interest as compound interest is based on the principal amount and the interest accumulates on it every period.
$A = P{\left( {1 + \dfrac{r}{100}} \right)^{nt}}$
Where, $A = $ final amount
$P = $ initial principal balance
$r = $ interest rate
$n = $ number of times interest applied per time period
$t = $ number of times period elapsed
Complete step-by-step answer:
In the first case we have 5 year time and an amount of 24000 and principal amount is 12000. So, by applying the above mentioned formula we will get,
24000 = 12000${\left( {1 + \dfrac{r}{{100}}} \right)^5}$
$
\Rightarrow \dfrac{{24000}}{{12000}} = {\left( {1 + \dfrac{r}{{100}}} \right)^5} \\
\Rightarrow 2 = {\left( {1 + \dfrac{r}{{100}}} \right)^5} \\
$
We have to find out the value of compound interest after 20 years. For that the value of exponent must be 20.
Multiply the exponent of both sides by 4
${2^4} = $ ${\left( {{{\left( {1 + \dfrac{r}{{100}}} \right)}^5}} \right)^4}$
16$ = {\left( {1 + \dfrac{r}{{100}}} \right)^{20}}$
Multiply P that is 12000 on both sides,
$16 \times 12000 = {\left( {1 + \dfrac{r}{{100}}} \right)^{20}} \times 12000$
We can see that here ${\left( {1 + \dfrac{r}{{100}}} \right)^{20}} \times 12000$ is the amount formula for 20 years.
So,
Amount $ = {\text{ 12000}}\left( {16} \right) = 192000$
After 20 years it will become Rs. 192000.
$\therefore $ Option B is correct.
Note: In this particular question, to find out the value of compound interest we have to use the general formula for compound interest. We can easily solve this question by deriving the amount formula like we did in the question. Also it is important to note that compound interest is different from simple interest as compound interest is based on the principal amount and the interest accumulates on it every period.
Recently Updated Pages
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Select the correct plural noun from the given singular class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
The sum of three consecutive multiples of 11 is 363 class 7 maths CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How many squares are there in a chess board A 1296 class 11 maths CBSE