# 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 = Pâˆ™Eâˆ™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

Example
What is the effective rate of interest when â‚¹10,000 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 â€“ 1 â‡’ E = (1.025)4 â€“ 1 = 10.38%