Compute the compound interest on Rs 1600 for 2 years at 10% per annum compounded annually

In what time will the sum of Rs. 1600 at 5% p.a. CI amounts to Rs. 1764?A. 1B. 1.5C. 2D. 3

Inhaltsverzeichnis Show

In what time will the sum of Rs. 1600 at 5% p.a. CI amounts to Rs. 1764?A. 1B. 1.5C. 2D. 3
Related Videos
How much would a sum of 16000 amount to in 2 years at 10% per annum if the interest is compounded half yearly?
What is the interest earned on Rs 1000 for 2 years at 10% per annum compound interest compounded annually?
What is the compound interest on Rs 1600 at 25% per annum of 2 years compounded annually?
What does 10% compounded annually mean?

Answer

Verified

Hint:
We know that the interest on the given principal is being compounded annually. So let use the formula of compound interest which is given below:
\[A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}\], where P is the principal amount, R is the rate of interest and T is the time taken.

Complete step by step answer:
It is given in the problem that the principal amount is Rs.1600, the rate of interest is 5% compounded annually and the total amount becomes Rs.1764.
We have to find the time taken in which the principal rises to the amount Rs.1774
According to the question, we know that the sum invested is Rs. 1600 at a rate of 5% compounded annually. Assume the principal amount as P and the rate of interest
$P = Rs.1600$and$R = 5\% p.a.$
We need to calculate the time in which the principal rises to the amount Rs. 1774
\[A{\text{ }} = {\text{ }}Rs.{\text{ }}1774\]
We have the formula of the amount is:
\[A = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}\]
Substituting the values of P, R, and A we get,
$1764 = 1600{\left( {1 + \dfrac{5}{{100}}} \right)^T}$
Simplifying the above equation:
$ \Rightarrow \dfrac{{1764}}{{1600}} = {\left( {\dfrac{{21}}{{20}}} \right)^T}$
$ \Rightarrow \dfrac{{441}}{{400}} = {\left( {\dfrac{{21}}{{20}}} \right)^T}$
$ \Rightarrow {\left( {\dfrac{{21}}{{20}}} \right)^2} = {\left( {\dfrac{{21}}{{20}}} \right)^T}$
By the law of exponents, we know that when the bases are the same across the equal too, the powers are equal. Thus we have,
$T = 2$
Hence, the principal will take 2 years to reach the amount to Rs.1764.
Therefore, option (C) is correct.

Note: The simple interest is cheaper than the compound interest because the simple interest applies to the whole amount for the whole time but in the case of compound interest, we have to pay the interest on the interest.

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

Previous Year Paper 2012 (L)

What is the compound interest ...

Updated On: 27-06-2022

UPLOAD PHOTO AND GET THE ANSWER NOW!

Text Solution

Rs.700Rs. 750Rs. 800Rs. 900

Answer

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

647944056

200

9.8 K