Lesson Relation between Simple Interest and Compound Interest

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Source code of 'Relation between Simple Interest and Compound Interest'

This Lesson (Relation between Simple Interest and Compound Interest) was created by by Shruti_Mishra(0)

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About Shruti_Mishra: I am a maths graduate from India and am currently persuing masters in Operations Research.

<a href="simple_interest2.lesson">Simple Interest</a> and <a href="compound_interest2.lesson">Compound Interest</A> remains the same for the first year of transaction as there is no accumulated interest till then.

E.g. Suppose ‘A’ borrowed 10000$ from ‘B’ for a period of 5 yrs at 10% simple interest and ‘C’ also borrowed 10000$ from ‘B’ for the period of 5 yrs at 10% <a href="interest_rate.lesson">interest rate</a> compounded annually.

During the first year of transaction both ‘A’ and ‘C ‘will be paying the same amount of interest to ‘B’.

A’s Interest 
Recalling the Formula
<center> {{{Interest = (Principal * Interest * time) /100}}}, where time = 1
</center>
Interest = [10000 * .10 * 1]/100 = 1000

B’s Interest
Recalling the Formula

<center>
{{{Amount = Principal + interest}}}
{{{Amount = Principal ((1 + Rate) ^ Years)}}}, where Years = 1
</center>
Amount = 10000 [(1 + .1) ^1] = 11000
Interest = Amount – Principal = 11000 – 10000 = 1000

So in both the cases the same interest is being charged.

How to find <a href="interest_rate.lesson">rate of Interest</A> from the given <a href="simple_interest2.lesson">Simple Interest</A> and <a href="compound_interest2.lesson">Compound Interest</A>?

The interest will remain the same for all the years now i.e. if the contract will be of 5 years, then every year 1000 will be charged as an interest. At the end of the 5th year the total amount will be the principal (10000) itself and the interest (1000 * 5) making a sum of 15000.

We can think of the <a href="compound_interest2.lesson">compound interest</A> as the series of the back to back simple interest. The <a href="compound_interest2.lesson">compound interest</A> is the interest charged on the accumulated <a href="simple_interest2.lesson">simple interest</A> till then.

Example: A pays Rs 200 as <a href="simple_interest2.lesson">Simple Interest</A> for two years and B pays 220 as <a href="compound_interest2.lesson">Compound Interest</A> for two years. The rate of interest and the Principal is same for both the transaction. What is the rate of interest being charged?

As we know the simple interest is same for all the years. Hence the interest for two years will be 200/2 = 100.

Now the simple interest and the compound interest remains the same for the first year hence compound interest will be 100 for the first year and for the second year it will be 220 – 100 = 120.

This sum of 120 is comprised of [Fixed Interest + Interest on interest] i.e. [100 + 20]. This 20 is charged on Rs 100, therefore the rate of interest will be 20/100 = .05 or 5 %

Also see: 
<a href="interest_rate.lesson">Basics of Interest Rates and its uses</A>
<a href="simple_interest2.lesson">Simple Interest</A>
<a href="compound_interest2.lesson">Compound Interest</A>