Like us!

Have a Look!

WhatsApp Message

Share Link

Compound Interest Compounded Annually

Comparing Quantities III - Concepts

Simple Interest

Compound Interest Compounded Annually

Compound Interest Different Rates

Compound Interest Time in Fractions

Compound Interest Half Yearly

Compound Interest Quarterly

Inverse Problems on Compound Interest - Principal

Inverse Problems on Compound Interest - Rate

Inverse Problems on Compound Interest Time Period

Problems on Population Growth

Problems on Depreciation

Class - 9th Aus Edu Subjects

Concept Explanation

Compound Interest Compounded Annually

Definition: Compound interest is calculated as a percentage as a total amount a the end of the previous compounding period.

Formula:

First Type: $F_{v} = P_{v}(1 + i )^{n}$ ,

where $F_{v}$ = Future Value

$P_{v}$ = Present Value or Original Amount

$i$ = Annual Interest Rate as a Decimal

$(i + 1)$ = multiplier

n = number of years of investment

Illustration: What will Rs 5000 invested at 8% p.a compound interest amount to after 2 years ?

Solution : An interest rate of 8% indicates that i = 0.08.

For 2 years , n = 2 and so $F_{v} = P_{v}(1 + i )^{n}$ = Rs 5000 $times$ $(1.08)^{2}$ = Rs 5832

Second Type:

To find interest only, we use

Compound interest = $F_{v}$ - $P_{v}$

Illustration: How much interest is earned according to the above example1 .

Solution : interest earned = $ 5832 - $ 5000 = $ 832

now , To Find Compound Interest (CI) when Interest is Compounded Annually:

In such cases where interest is compounded yearly, the interest accrued during the first year is added to the principal and the amount so obtained becomes the principal for the second year. The amount at the end of the second year becomes the principal for the third year, and so on.

Illustration: Find the compound interest on Rs 25000 for 3 years at 6% per annum, compounded annually.

Solution: Principal for the first year = Rs. 25000.

$Interest ;for; the; first; year = frac{25000;X;6;X;1}{100}= Rs. 1500.$

Amount at the end of the first year = 25000 + 1500 = Rs 26500.

Principal for the second year = Rs. 26500.

$Interest ;for; the; second; year = frac{26500;X;6;X;1}{100}= Rs. 1590.$

Amount at the end of the second year = Rs 26500 + 1590 = Rs 28090.

Principal for the third year = Rs 28090.

$Interest ;for; the; third; year = frac{28090;X;6;X;1}{100}= Rs. 1685.40$

Amount at the end of the third year = 28090 + 1685.40 = Rs 29775.40.

Therefore, compound interest = 29775.40 - 25000 = Rs 4775.40.

Compound Interest By Formula:

$Amount= Principalleft [1+frac{Rate}{100} right ] ^{time}$

$Compound ;Interest= Amount- Principal$

For the above example:

Principal = 25000

Rate= 6%

time= 3 years

$Amount= Principalleft [1+frac{Rate}{100} right ] ^{time}$

$Amount= 25000left [1+frac{6}{100} right ] ^{3}$

$= 25000left [1+frac{3}{50} right ] ^{3}$

$= 25000left [frac{53}{50} right ] ^{3}$

$= 25000 X ; frac{53}{50};X; frac{53}{50};X; frac{53}{50}$ $= frac{53;X;53;X; 53}{5}=frac{148877}{5}=29775.4$

Therefore, compound interest = 29775.40 - 25000 = Rs 4775.40.

Sample Questions

(More Questions for each concept available in Login)

Question : 1

Find the compound interest on Rs. 12000 for 3 years at 10% p.a. compounded annually.
A. 3972	B. 3565	C. 6586	D. 4587
Right Option : A
View Explanation

Question : 2

Find the amount at the end of 2 years of Rs.1000 at 4% compounded annually.
A. Rs.1081.50	B. Rs.1081.70	C. Rs.1081.80	D. Rs.1081.60
Right Option : D
View Explanation

Question : 3

A man borrowed Rs. 3125 for CI and it amounted to Rs. 4500 in 2 years. The rate of CI per annum is :
A. 30%	B. 25%	C. 20%	D. 15%
Right Option : C
View Explanation

Video Link - Have a look !!!

Language - English

Students / Parents Reviews [20]

The experience was nice. I studied here for three years and saw a tremendous change in myself. I started liking subjects like English and SST which earlier I ran from. Extra knowledge gave me confi...

Aman Kumar Shrivastava

10th

Abhyas academy is great place to learn. I have learnt a lot here they have finished my fear of not answering.It has created a habit of self studying in me.The teachers here are very supportive and helpful. Earlier my maths and science was good but now it has been much better than before.

Barkha Arora

10th

It was a good experience with Abhyas Academy. I even faced problems in starting but slowly and steadily overcomed. Especially reasoning classes helped me a lot.

Cheshta

10th

We started with lot of hope that Abhyas will help in better understnding of complex topics of highers classes. we are not disappointed with the progress our child has made after attending Abhyas. Though need to mention that we expected a lot more. On a scale of 1-10, we would give may be 7.

Manya

8th

My experience was very good with Abhyas academy. I am studying here from 6th class and I am satisfied by its results in my life. I improved a lot here ahead of school syllabus.

Ayan Ghosh

8th

My experience with Abhyas academy is very nice or it can be said wonderful. I have been studying here from seven class. I have been completing my journey of three years. I am tinking that I should ...

Hridey Preet

9th

Abhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.

Manish Kumar

10th

About Abhyas metholodology the teachers are very nice and hardworking toward students.The Centre Head Mrs Anu Sethi is also a brilliant teacher.Abhyas has taught me how to overcome problems and has...

Shreya Shrivastava

8th

Abhyas institute is one of the best coaching institute in the vicinity of Ambala Cantt area. The teachers of the institute are well experienced and very helpful in solving the problems of the students.The good thing of the institute is that it is providing extra classes for the students who are w...