Effective Interest Rate and Nominal Interest Rate

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

Calculation of Nominal Interest Rate

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

Nominal Interest Rate = (Effective Interest Rate / n) x m

Where n is the number of compounding periods per year and m is the number of years.

In this case, the effective rate of interest is 12% per annum and the interest is compounded quarterly. Therefore, we have:

n = 4 (compounding periods per year)

m = 1 (one year)

Effective Interest Rate = 12%

Nominal Interest Rate = (12% / 4) x 1 = 3%

Therefore, the nominal interest rate per annum is 3%.

Explanation

When interest is compounded, the interest earned in each compounding period is added to the principal, and interest is then calculated on the new principal amount. The more frequently interest is compounded, the higher the effective interest rate will be compared to the nominal interest rate.

In this case, the effective rate of interest is 12% per annum, which means that if the interest were not compounded, the borrower would pay or the lender would earn 12% per annum. However, since the interest is compounded quarterly, the borrower would actually pay or the lender would earn more than 12% per annum.

The nominal interest rate, which is the rate stated or advertised without considering compounding, is 3% per annum. This means that the borrower would pay or the lender would earn 3% per annum if interest were not compounded. However, since interest is compounded quarterly, the effective interest rate is higher at 12% per annum.

12=[(1+r/400)^4-1]×100
12÷100+1=(1+r/400)^4
1.12=(1+r/400)^4
take two time root for power 1/4
and then calculate r.