At what rate per cent compound interest does a sum of money becomes 1.44 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?

Inhaltsverzeichnis Show

At what rate percent compound interest, does a sum of money become 1.44 times of itself in 2 years?
Related Videos
At what rate percent compound interest does a sum of money becomes 1.44 times of itself?
At what rate per cent will a sum of 4000 yield 1 324 as compound interest in3 years?
At what rate per cent of simple interest does a sum of money double itself in 12?
At what rate percent compound interest does a sum of money becomes 9 times 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.

Getting Image
Please Wait...

Course

NCERT

Class 12Class 11Class 10Class 9Class 8Class 7Class 6

IIT JEE

Exam

JEE MAINSJEE ADVANCEDX BOARDSXII BOARDS

NEET

Neet Previous Year (Year Wise)Physics Previous YearChemistry Previous YearBiology Previous YearNeet All Sample PapersSample Papers BiologySample Papers PhysicsSample Papers Chemistry

Download PDF's

Class 12Class 11Class 10Class 9Class 8Class 7Class 6

Exam CornerOnline ClassQuizAsk Doubt on WhatsappSearch DoubtnutEnglish DictionaryToppers TalkBlogJEE Crash CourseAbout UsCareerDownloadGet AppTechnothlon-2019

Logout

+91

Home

English

Class 14

Maths

Chapter

Compound Interest

If a sum of money compounded a...

Updated On: 27-06-2022

UPLOAD PHOTO AND GET THE ANSWER NOW!

Text Solution

Answer : `20%`

Answer

Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

643656089

1.8 K