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Effective Rate of Interest

If interest is compounded more than once in a year, then the equivalent annual rate of interest compounded annually is known as the effective rate of interest.
 

Let ₹100 be invested for a year at the rate of 5% per annum compounded semi-annually.
 

The amount at the end of the year will be

 

Description: 57254.png 

 

Therefore, C.I. at the end of the year = 105.0625 – 100 = ₹5.0625

 

We can calculate the effective rate of interest in this case by making the use of the following formula:

 

I = PET

 

where I is the interest

         P is the principal

         E is the effective rate of interest

         T is the time period

 

Substituting the values in the above relation, we have

 

Description: 57267.png 

We can see that, if interest is computed more than once in a year, then the effective rate of interest will be more than the actual rate of interest.

 

The effective rate of interest can be computed directly using the relation

 

E = (1 + r)n – 1

 

where E is the effective rate of interest

         r is the actual rate of interest in decimals (i.e.r = R/100)

         n is the number of conversion periods
 

Example
What is the effective rate of interest when ₹10,000 is deposited at 10% p.a. compounded quarterly?
Solution
Given, R = 10% p.a. or r = 0.1 p.a., n = 4 (since interest is compounded quarterly)
E = (1 + 0.1/4)4 – 1 ⇒ E = (1.025)4 – 1 = 10.38%





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