# Difference between real and nominal rates of interest.

Nominal interest rates measure the rate at which money invested grows. If you invest £1,000 in a bank account at a nominal rate of 10% the bank promises to pay £1,100 at the end of the year. The nominal rate of interest offered by the bank is certain but the bank makes no promises on what the £1,100 can actually buy. This is because prices of goods and services change; an overall sustained increase in general prices is called inflation.

Thus the real rate of interest is the nominal interest rate adjusted for inflation. The real rate of interest therefore measures the real value of the £1,100 invested in terms of its buying power. If inflation is 5% then a bar of chocolate that costs £1.00 last year will now cost £1.05. Inflation leads to the decline in the value of your money in terms of what you can purchase.

For example if inflation is 5% and the nominal rate of interest is 10% on a bank account the real interest rate based on approximation is 10% - 5% = 5% therefore the real value of a £1,000 invested for a year will be £1,050.

The formula for calculating the accurate real rate of interest is:

1 + real interest rate = 1 + nominal rate

1 + inflation

= 0.047 / 4.7% real rate of interest

Therefore the nominal interest rate is expressed in money terms and the real rate of interest is the buying power of money.

**Do changes in nominal interest rate only have an impact on the firm’s investment decisions if they are accompanied by a change in real interest rate? **

Based on the assumption that firms use the real rate of interest as a discount rate to evaluate the NPV of projects, any change in nominal rates of interest should be adjusted for inflation to give the real rate of interest.

Inflation is an important factor that can have a big impact on future cash flows, so need to be considered when making investment decisions.

For example if a company was evaluating the following project K:

Yr 0

Outlay

£10,000

Yr 1

Cash flow 1

£5,000

Yr 2

Cash flow 2

£5,800

**Scenario 1**

Discount rate = real rate approximation:

q 10% nominal interest rate / 5% inflation

q 10% - 5% = 5 % real rate of interest (approx)

Year

Cash flow

PV at 5%

Yr 0

(£10,000)

(£10,000)

Yr 1

£5,000

£4,761

Yr 2

£5,800

£5,261

## NPV

**£22 Accept**

## Scenario 2

If there is a 1% increase in nominal interest rate and inflation is constant it will have an impact on the firms decision as the real rate of interest has increased by 1% to 6%.

Year

Cash flow

PV at 6%

Yr 0

(£10,000)

(£10,000)

Yr 1

£5,000

£4,716

Yr 2

£5,800

£5,162

## NPV

**(£122) Reject**

In this case the real rate of interest has changed to 6%, which has lead to a negative NPV and will result in the company’s rejecting this project.

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