The article at hand is a part of our 60 days study plan on BBA & HM entrance exams. In this study plan, we will provide all the important Quantitative Ability-related topics and articles in a crisp and easy-to-understand format which will save your time of note-making. Now, all you need to do is read the article and solve the quiz associated with it. This will enhance your understanding of the topic in a much better way.
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To make the chapter easy for you all, we are providing you all some Important Short Tricks to solve Compound Interest Questions which will surely make the chapter easy for you all.
Important Short Tricks to solve Compound Interest Questions
Compound Interest:- Sometimes it so happens that the borrower and the lender agree to fix up a certain unit of time, say yearly or half-yearly or quarterly to settle the precious account.
In such cases, the amount after first unit of times becomes the principal for the second unit the amount after second unit becomes the principle for the third unit and so on.
After a specified period, the difference between the amount and the money borrowed is called the Compound Interest (abbreviated as C.I.) for that period.
Important Facts & Formulas on Compound Interest
Case 1: Let principle = P, time = n years and rate = r% per annum and let A be the total amount at the end of n years, then
Example: Albert invested an amount of Rs.8000 in a fixed deposit scheme for 2 years at compound interest rate 5 p.c.p.a. how much amount will Albert get on maturity of the fixed deposit.
Solution:
Amount = Rs.
= Rs.
Case 2: When compound interest is reckoned half-yearly.
If the annual rate is r% per annum and is to be calculated for n years, then in this case, rate = (n/2 %) half-yearly and time = (2n) half-yearly.
From the above we get
Example: Sam investment Rs.15,000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be.
Solution:
P = Rs. 15000; R = 10% p.a = 5% half-year, T = 1 year = 2 half year
Amount = Rs
= Rs.16537.50
Case 3: When compound interest is reckoned quarterly.
In this case, rate = (r/4 %) quarterly and time = (4n) quarter years.
As before,
Example:
Find the compound interest on Rs. 15,625 for 9 months at 16% per annum compounded quarterly.
Solution:
P = Rs. 15625, n= 9 months = 3 quarters, R = 16% p.a. = 4% per quarter.
Amount = Rs.
= Rs.17576
C.I = Rs. (17576 – 15625 ) = Rs. 1951.
Note: The difference between the compound interest and the simple interest over two years is given by
or
Case 4: When interest is compounded annually but time is in fraction, say years.
Amount =
Example:
What is the difference between the compound interest on Rs. 5000 for at 4% per annum compounded yearly and half-yearly?
Solutions:
C.I. when interest is compounded yearly
= Rs.
= Rs.5304
C.I. when interest is compounded half-yearly
Difference = Rs.(5306.04 – 5304 ) = Rs.2.04.
Case 5: when rates are different for different years say for 1st, 2nd, 3rd year respectively.
Then, amount =
Example:
The population of Jhumri Tilaiya increases by 10% in the first year, it increases by 20% in the second year and due to mass exodus, it decreases by 5% in the third year. What will be its population after 3 years, if today it is 200,000?
Solution:
Population at the end of 1 year will be 10,000 + 10% of 10,000= 11,000
At the end of second year it will be 11,000 + 20% of 11,000 = 13,200
At the end of third year it will be 13,200 – 5% of 13, 20 = 12,540
Case 6: Present worth of Rs.x due n years hence is given by:
Present Worth =
Example:
The principle that amounts to Rs.4913 in 3 years at per annum compound interest compounded annually, is :
Solution:
Principle = Rs.
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