At what rate percent compound interest does a sum of money becomes 144 times of itself in 2 years?

At what rate percent compound interest, does a sum of money become 1.44 times of itself in 2 years?

Answer

Verified

Hint: First, we will let the principal sum of money as ‘P’ and the rate of interest as ‘R’. we will use the conditions given in the question and formula of compound interest to form a different equation. And by solving those equations we will find the rate of interest.

Complete step-by-step solution:
Let the principal sum of money be ‘P’.
Let the rate of interest compounded annually be ‘R’.
Given: the amount becomes 1.44 times the principal amount in the span of 2 years.
So, \[A = 1.44 \times P\]----- (1)
By using compound interest formulas. We get,
$A = P \times {\left( {1 + \dfrac{R}{{100}}} \right)^2}$----- (2)
From equation 1 and 2. We get,
$1.44 \times P = P \times {\left( {1 + \dfrac{R}{{100}}} \right)^2}$
$\Rightarrow 1.44 = {\left( {1 + \dfrac{R}{{100}}} \right)^2}$
Squaring on both sides.
$\sqrt {1.44} = \left( {1 + \dfrac{R}{{100}}} \right)$
Value of square root 1.44 is 1.2.
$1.2 = \left( {1 + \dfrac{R}{{100}}} \right)$
We can also write 1.2 as 1 + 0.2.
$1 + 0.2 = \left( {1 + \dfrac{R}{{100}}} \right)$
We can write 0.2 as 2/10.
$1 + \dfrac{2}{{10}} = \left( {1 + \dfrac{R}{{100}}} \right)$
$\Rightarrow \dfrac{2}{{10}} = \dfrac{R}{{100}}$
$\Rightarrow 2 = \dfrac{R}{{10}}$
$\Rightarrow R = 2 \times 10$
$\Rightarrow R = 20\% $
So, the rate percent compound interest is $20\%.$

Note: Compound interest (or compounding interest) is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. The rate at which compound interest accrues depends on the frequency of compounding, such that the higher the number of compounding periods, the greater the compound interest. Compound interest is calculated by multiplying the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one. The total initial amount of the loan is then subtracted from the resulting value.

the question is at what rate percent compound interest does a sum of money becomes does a sum of money becomes 1.4 times of itself into your site so now let the sum of money becomes topi so we can write the principal principal amount here we're having is and as the question is that the sum of the sum of money becomes 1.4 times of itself this means we can say that a b having a is equals to 1.4 times of itself that right and it is also given that into years so we're having time that is represented by a small of t is equals to to write we know that there is a form that it is equals to 3 to 1 + r100 oldest power bi report that we'd be having the social so we can write your place of this week

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we can see that you read read person that is are is equals to 20% and hence we can see that this is our final answer thank you

Let Principal = Rs. y
Then Amount= Rs 1.44y
n= 2 years

∴ Amount = `"P"( 1 + "r"/100 )^n`

⇒ 1.44y  = `y( 1 + r/100)^2`

⇒ `[1.44y]/y = ( 1 + r/100)^2`

⇒ `36/25 = ( 1 + r/100)^2`

⇒ `( 6/5 )^2 = ( 1 + r/100)^2`

On comparing,
`6/5 = 1 + r/100`

On solving, we get
 r = 20 % 

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