Question

at what rate per cent compound interest does a sum of money become 1.44times of itself in 2years

Answer 1

$\huge\rm\orange{Given:-}$

Time = 2 years

Let the sum = x

And the amount = 1.44 x

$\huge\rm\orange{To~Find}$

Rate = ?

$\huge\rm\red{Solution:-}$

As we know

Amount = $P[1+\dfrac{r}{100}]^n$

We are having amount, sum, time. So, put the values.

$\rm{ 1.44x = x \left[ 1 + \dfrac{r}{100} \right]^2 }$

(After cutting 'x' remove the decimal point.)

$\dfrac{144}{100}$ = [$1+\dfrac{r}{100}]^2$

$(\dfrac{12}{10})^2$ = [1+$\dfrac{r}{100}]^2$

▪Remove the powers as they are same.

$\dfrac{12}{10}$ = $1 + \dfrac{r}{100}$

$\dfrac{12}{10}$ -1 = $\dfrac{r}{100}$

$\dfrac{12-10}{10}$ = $\dfrac{r}{100}$

$\dfrac{2×100}{10}$ = r

Answer ➣

Rate = 20%

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$\huge\sf\red{Additional}$

$\huge\sf\red{Information}$

▪ Formula to find C.I. if amount and principal are given.

➣ C.I. = A - P

▪ Formula to find C.I. if principal and time are given.

➣ C.I. = $P[({\dfrac{r}{100}})^n-1]$

▪ Formula to find Amount if principal and Compound Interest are given.

➣ A = C.I. + P

▪ Formula to find Interest.

➣ S.I. = $\dfrac{P×R×T}{100}$