# Nominal Interest Rate

Nominal interest rate is the interest rate which includes the effect of inflation. It approximately equals the sum of real interest rate and inflation rate.

Loans and investments mostly quote a nominal interest rate because it is the rate which is applied to the principal balance to arrive at interest expense. However, it is not the actual cost borne by the borrower. Since inflation erodes the value of money, the real maturity value of loan decreases with inflation. This results in a much lower real interest rate. Nominal interest rate overstates the cost of money for the borrower and rate of return for the lender.

Nominal annual interest rate can also refer to the annual quoted interest rate which is not adjusted for the effect of multiple compounding periods per year. This interest rate is more appropriately called the annual percentage rate. The opposite of such a nominal interest rate is the effective interest rate.

## Formula

When we have information about present value (PV), future value (FV) and number of time periods (NPER), we can work out the nominal interest rate using the following formula:

$$\text{r} _ \text{n}=\left(\frac{\text{FV}}{\text{PV}}\right)^\frac{\text{1}}{\text{NPER}}-\text{1}$$

If we have information about real interest rate (rr) and inflation rate (i), the nominal interest rate (rn) can also be worked out using the Fisher equation:

$$\text{r} _ \text{n}=(\text{1}+\text{r} _ \text{r})(\text{1}+\text{i})-\text{1}$$

## Example

Your company wants to raise $20 million. It has received two proposals. Bank A has offered to provide$20 million against a promissory note with maturity value of \$23 million due 2 years from now. Bank B requires a real interest rate of 4%. If the expected inflation rate for next 2 yeas is 3%, find out which bank has offered a lower interest rate. The interest on both loans is compounded annually.

### Solution

The nominal annual interest rate on the Bank A loan equals 7.24%.

$$\text{r} _ \text{n}=\left(\frac{\text{\23M}}{\text{\20M}}\right)^\frac{\text{1}}{\text{2}}- \text{1}=\text{7.24%}$$

Since the annual real interest rate is 4% and expected inflation rate is 3%, the nominal interest rate on the Bank B loan can be obtained using the Fisher equation:

$$\text{r} _ \text{n}=(\text{1}+\text{4%})(\text{1}+\text{3%})-\text{1}=\text{7.12%}$$

It shows that Bank B has a lower nominal interest rate.