Study Note on Basics of Compound Interest

By Gaurav Mohanty|Updated : December 20th, 2021

Know the Basics of Compound Interest.

Compound Interest is one of the toughest chapters which leaves candidates a bit confused and most of the aspirants leave these questions untouched.

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 the first unit of times becomes the principal for the second unit the amount after the 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 a compound interest rate of 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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