The Effective Rate of Interest and Nominal Rate of Interest

The effective rate of interest is the actual rate of interest earned or paid on an investment or loan, taking into account the effects of compounding. On the other hand, the nominal rate of interest is the stated rate of interest on an investment or loan, without considering the effects of compounding.

Given Information

- Effective rate of interest: 12% per annum
- Compounding frequency: quarterly

Calculating the Nominal Rate of Interest

To calculate the nominal rate of interest, we need to use the formula:

Nominal rate of interest = [(1 + r/n)^n - 1] * 100

Where:
- r is the effective rate of interest
- n is the number of compounding periods per year

In this case, the effective rate of interest is 12% per annum and the compounding frequency is quarterly. Therefore, the number of compounding periods per year is 4.

Substituting the values into the formula, we have:

Nominal rate of interest = [(1 + 0.12/4)^4 - 1] * 100

Simplifying the equation, we get:

Nominal rate of interest = [(1 + 0.03)^4 - 1] * 100
Nominal rate of interest = (1.03^4 - 1) * 100
Nominal rate of interest = (1.1255 - 1) * 100
Nominal rate of interest = 0.1255 * 100
Nominal rate of interest = 12.55%

Therefore, the nominal rate of interest per annum, when the effective rate of interest is 12% per annum and interest is compounded quarterly, is 12.55%.

Conclusion

The nominal rate of interest is the stated rate of interest without considering the effects of compounding, while the effective rate of interest takes into account the compounding frequency. By using the formula, we can calculate the nominal rate of interest based on the effective rate of interest and the compounding frequency. In this case, the nominal rate of interest is 12.55% per annum.

12.55%