Calculating the Compound Rate of Interest

The nominal rate of interest is the interest rate per year. The rate of compound interest is commonly expressed as a nominal rate of interest. For example in 10% compounded quarterly, 10% refers to the nominal rate of interest.

To calculate the nominal rate of interest, simply multiply the rate of interest per period by the number of periods per year.

Nominal Rate = Rate per Period x Periods per Year

In order to compute the nominal rate of interest, the rate of interest per period should be determined.

Here are the steps in order to solve the nominal rate of interest:

• 1) Future amount, principal, periods per year and number of years should be given.
• 2) Divide the future amount by the principal amount.
• 3) Get the nth root of the quotient where n is the number of periods.
• 4) Subtract the root by 1.
• 5) Multiply the difference by the periods per year.

The formula to find the nominal rate of interest can be derived using the formula,

Future Amount = Principal x `(1+text(Rate per Period))^text(Number of Periods)--- (I)`

As we know that,

Nominal Rate = Rate per Period x Periods per Year

So,

Replacing "Rate per period" in Equation (I):

Future Amount=Principal x `(1+text(Nominal Rate)/text(Periods per Year))^text(Number of Periods)`

`text(Future Amount)/text(Principal) = (1+text(Nominal Rate)/text(Periods per Year) )^text(Number of Periods) --- (II)`

Let n be the number of periods, then,

`text(Future Amount)/text(Principal)= (1+text(Nominal Rate)/text(Periods per Year))^n`

Nominal Rate of Interest = Periods per Year x `(n sqrt(text(Future Amount)/text(Principal))-1)`

Where n is the total number of periods.