Interest Rates, Inflation and the Fisher Equation

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Inflation is an increase in the general price level. Expected inflation rate is

� − � � = ! ! �!

Quick Maths If the current price level is £1, meaning that the average good costs £1, and the expected price level is £1.10 next year the inflation is £.!"!£ = 10% £

The Nominal Interest Rate, R is in terms of money and includes inflation. If you save £1 today then you will receive £(1+R) pounds tomorrow.

Economists often say that the Real Interest Rate, r is in terms of goods - if you save one unit of goods today then you will receive (1 + r) units of goods tomorrow – which is very unclear as banks don’t tend to let you put you car into a vault and return it with an extra steering wheel as interest.

Nominal Interest Rates vs. Real Interest Rates The real interest rate accounts for inflation whereas the nominal interest rate does not. Here’s an example to illustrate the difference:

Lets clear this up: Sally the Squirrel has £100 to save for next year’s cold winter. A nut costs £4 today so she could have purchased 25 nuts this year and buried them away. But like many squirrels she is somewhat forgetful. Instead she goes to her bank - NutWest - and they offer her a savings account with 40% interest (R = 40%). Banks always offer rates in nominal terms as they don’t understand economics. Plus this way they get to rob poor squirrels blind. Poor Sally saves her £100 thinking she’s going to receive enough interest to buy an extra 10 nuts next year, which would be 40% more nuts. Poor Sally should have studied economics. Due to many squirrels unable to find their buried nuts the price of nuts rises greatly over the year. As nuts are the only good in the squirrel economy, this is inflation, and the price rises a whooping 25% so that now nuts cost £5! When Sally goes back to the bank she receives her £100 plus £40 interest – a 40% return on her money. However, when she goes to spend this £140 she finds that it only buys her 28 nuts at the new price of £5 per nuts. She feels robbed. The 40% interest rate was nominal because it did not account for inflation. In www.theprofs.co.uk 1 First-Class University Tutors terms of goods (as economists would say), she was not able to buy 10 more nuts, but only 3 more nuts. So the real interest rate, telling us what our money can really afford in terms of goods, and which accounts for inflation, was lower. In this example, she could previous afford 25 nuts, now she can afford 28 so 28 ÷ 25 = 1.12 (r=12%)

In the real world, where inflation and interest rates are much smaller than the above example, then an accurate approximate for the Fisher Equation , which describes the relationship between the real, nominal and inflation rates is.

� = � + �

If inflation is positive, which it generally is, then the real interest rate is lower than the nominal interest rate. If we have deflation, meaning that the inflation rate is negative, then the real interest rate will be larger.

For an exact mathematical relationship, read on:

The real interest rate is the interest from savings in terms of goods rather than money. We must convert goods into money, invest the money and then convert back into goods at the new prices.

Ø One unit of goods buys P units of today’s money Ø Saving P units of unit today returns you �!(1 + �) units of tomorrow’s money. ! Ø �!(1 + �) units of tomorrow’s money will buy you goods tomorrow !!

Therefore

� × (1 + �) 1 + � = ! �!

(1 + �) 1 + � = �! �!

(1 + �) 1 + � = (1 + �)

or (1 + �)(1 + �) = (1 + �)

Note: the approximation works because �� is negligible because both r and i are such small numbers and then the 1s cancel out.