Identify how to calculate nominal interest rates and real interest rates. Assume that you put $100 in the bank. Use numeric examples to explain three different scenarios in which the REAL interest rate is positive, stays the same, and is negative.

If real interest rate is positive, its value given the inflation and nominal interest rate would be:  [(1.05 / 1.02) - 1 = 2.94%.

If $100 is deposited, the real interest rate would be $2.94 and nominal interest rate would be $5.

If real interest rate is negative, its value given the inflation and nominal interest rate would be:  [(1.02 / 1.05) - 1 = -2.86%.

If $100 is deposited, the real interest rate would be $-2.86 and nominal interest rate would be $2.

If real interest rate stays the same, its value given the inflation and nominal interest rate would be:  [(1.05 / 1) - 1 = 5%.

If $100 is deposited, the real interest rate would be $5 and nominal interest rate would be $5.

The equation used to determine the nominal interest rate is the Fisher equation: (1 + nominal interest rate) = (1 + real interest rate) x (1 + inflation rate)

Real interest rate = [(1 + nominal interest rate) /  (1 + inflation rate)] - 1.

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Please refer to Explanation

Explanation:

To answer this question we will assume that the Nominal Interest rate is equal to 10% then we can be free to manipulate the Real Interest Rate.

Now the Real Interest Rate is the Nominal Interest Rate adjusted for inflation in the following manner,

Real interest rate= Nominal interest rate - inflation rate.

Let's go through 3 scenarios now.

1. REAL interest rate is positive.

If the Real Interest rate is positive, that would mean that Inflation rate is LESS than the Nominal Interest rate.

Assuming the inflation rate is 5% then that would mean that real interest rate is,

= 10% - 5%

= 5%.

Seeing as you have $100 in the bank. If using Nominal Rates alone you would have earned,

= 100 * (1+0.1)

= $110

However with a rate that caters for inflation (Real Interest Rate) you would earn only,

= 100 * (1 + 0.05)

= $105

2. REAL interest rate stays the same

If the Real Interest rate does not change, that would mean that Inflation rate is EQUAL to Nominal Interest rate.

Assuming the inflation rate is 10% then that would mean that real interest rate is,

= 10% - 10%

= 0% meaning that there was no change.

You have that same $100 in the bank. If using Nominal Rates alone you would have earned,

= 100 * (1+0.1)

= $110

However with a rate that caters for inflation (Real Interest Rate) you would earn only,

= 100 * (1 + 0.00)

= $100

Your money in the bank would in REAL TERMS not have changed because whatever profit you made was wiped out by inflation.

3. REAL interest rate is negative.

If the Real Interest rate is negative, that would sadly mean that Inflation rate is MORE than the Nominal Interest rate.

Assuming the inflation rate is 15% then that would mean that real interest rate is,

= 10% - 15%

= -5%.

Seeing as you have $100 in the bank. If using Nominal Rates alone you would have earned,

= 100 * (1+0.1)

= $110

However with a rate that caters for inflation (Real Interest Rate) you would earn only,

= 100 * (1 - 0.05)

= $95

If inflation were to be catered for, the value of your money has actually decreased from $100 to $95 because inflation rose at a faster rate than nominal inflation. This means that the money you had can buy only 95% of what it could before.

This is why the Real Interest Rate is Important. It shows you whether you are actually making a profit based on the rate at which prices are rising in the Economy. It is crucial that the Real Rate is calculated so that you get adequate compensation for your Investment.

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