Effective rate of interest and effective rate of discount

Effective Rate of Interest

The Effective Rate of Interest is the true rate of interest that reflects the impact of compounding on the principal amount over a specified period.

The formula for the Effective Rate of Interest is:

i = (1 + (r / n))^n - 1

Where:

• r is the nominal annual interest rate (as a decimal),
• n is the number of compounding periods per year.

For example, if the nominal interest rate is 12% compounded monthly, the effective annual interest rate is:

i = (1 + (0.12 / 12))^12 - 1

Effective Rate of Discount

The Effective Rate of Discount is the rate that discounts the future value to find the present value. It is the reverse of the interest rate.

The formula for the Effective Rate of Discount is:

d = i / (1 + i)

Where:

• i is the effective rate of interest.

For example, if the effective rate of interest is 12%, the effective rate of discount would be:

d = 0.12 / (1 + 0.12) = 0.1071 or 10.71%