# 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 â‚¹100 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

Therefore, C.I. at the end of the year = 105.0625 â€“ 100 = â‚¹5.0625

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

*I* = *P*âˆ™*E*âˆ™*T*

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

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}* â€“ 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

*R*= 10% p.a. or

*r*= 0.1 p.a.,

*n*= 4 (since interest is compounded quarterly)

*E*= (1 + 0.1/4)

^{4}â€“ 1 â‡’

*E*= (1.025)

^{4}â€“ 1 = 10.38%