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Compound interest refers to the addition of interest to the principal amount. It is also termed as interest on interest and is the result of a re-investment of interest, rather than resulting in a payout. An example of it is the interest paid by the bank. In this case, the interest increases successively. Hence, we can conclude that the bank charges compound interest.
The questions based on Compound Interest include exams such as SBI PO, IBPS PO, SBI SO, IBPS Clerk, SBI Clerk, IBPS RRB, NABARD, SEBI, RBI, LIC AAO and SSC CGL. Usually, 2 to 3 questions based on Compound Interest are asked in the exam.
Compound Interest Questions PDF:
Compound Interest PDF Set 1
CI Level 1
Definition of Compound Interest
It is the interest which is calculated on the principal as well as the interest accumulated in case of the previous period or year. It is different from simple interest as in the case of simple interest, the interest is not added to the principal. It is used generally in the banking and finance sector. The application of compound interest can be used to compute, the increase or decrease of population and the rise or fall in the value of an item.
The formula for compound interest
The formula for compound interest is given below:
A = P (1 + R100) t
In this case,
A = Amount
P = principal
R = rate of interest
n = number of times the interest is compounded in a year
We can also compute Compound interest as,
Compound Interest = Amount – Principal
Examples of Compound Interest
1. Find compound interest on Rs. 7000 at 21% per annum for 2 years 4 months, compounded annually.
|Time = 2 years 4 months = 2||4||years = 2||1||years.|
Let principal = P, Rate = R% per annum, Time = n years.
When interest is compounded annually. then,
|Amount = P||(||1 +||R||)||n|
|So, amount = Rs||[||7000 ×||(||1 +||21||)||2||]||×||(||1 +||1/3 × 21||)]|
|⇒ Rs.||(||7000 ×||121||×||121||×||107||)|
So, C.I. = Rs. (10966.1 – 7000) ⇒ Rs. 3966.1.
Hence, option B is correct.
2. A certain amount of money is lent out at compound interest at the rate of 20% per annum for two years, compounded annually. It would give Rs. 482 more if the amount is compounded half yearly. Find the principle.
A Rs. 30000
B Rs. 10000
C Rs. 15000
D Rs. 25000
E None of these
Approach I: To solve this question, we can apply the net % effect formula
|x + y +||xy||%|
|= 20 + 20 +||20 × 20||= 44%|
Similarly, compounded half yearly at rate 10%, we get
|= 10 + 10 +||10 × 10||= 21%|
|And, 21 + 10 +||21 × 10||= 33.1%|
|And, 33.1 + 10 +||33.1 × 10||= 46.41%|
Now as per the question,
Difference between compound interest yearly and half yearly = 46.41 – 44 = 2.41%
Given, 2.41% ≡ 482
100% ≡ x
|⇒ x =||482 × 100||= 20,000|
When compounded annually, the amount received at the end of the period is
|A = P||[||1 +||r||]||n|
When compounded half yearly, the amount received at the end of the period is
|A = P||[||1 +||r/2||]||2n|
Let the principle be P.
Interest on this amount when compounded annually at the rate of 20% per annum = P [(1.20)2 − 1]
Interest on this amount when compounded half yearly = P [(1.10)4 − 1]
The difference between the two is Rs. 482
∴ P [(1.10)4 − 1] – P [(1.20)2 −1] = 482
∴ P [1.4641 – 1.44] = 482
∴ P = Rs. 20,000
Hence, option E is correct.