Question

Suppose we have a bond that sells for \(\$ 1,000 .\) The annual interest paid is \(\$ 80 .\) However, the monetary authorities have predicted that the general price level will increase next year by 5 percent. Given these facts, compute the; a) nominal interest rate. b) real interest rate.

Short answer

a) The nominal interest rate is 8%. b) The real interest rate is 3%.

Step-by-step solution

Compute the Nominal Interest Rate

This refers to the interest rate before taking inflation into account. It is derived from the formula: Nominal Interest Rate = (Annual Interest / Bond Price) * 100 Substitute the given values into the equation: Nominal Interest Rate = (\( \$80 / \$1000 \)) * 100

Solution to part (a) - The Nominal Interest Rate

Using the formula and values from Step 1, you calculate (\( \$80 / \$1000 \)) * 100 = 8%. Hence, the nominal interest rate is 8%.

Compute the Real Interest Rate

This refers to the interest rate that has been adjusted to remove the effects of inflation. It can be calculated using the Fisher equation: Real Interest Rate = Nominal Interest Rate - Inflation Rate Substitute the given values into the equation: Real Interest Rate = 8% - 5%

Solution to part (b) - The Real Interest Rate

Using the formula and values from Step 3, you calculate 8% - 5% = 3%. Hence, the real interest rate is 3%. This means that once the effect of expected inflation is removed, the purchasing power of your money has increased by 3% in real terms.

Key concepts

Nominal Interest Rate

To start, let's explore the concept of the nominal interest rate. This rate refers to the percentage that expresses the payment for the use of money over a period of time, without removing inflation from the picture. It represents the face value you receive as income from an investment like a bond.

In essence, the nominal interest rate is calculated before taking inflation into account, which can distort the real worth of the earnings. To illustrate, if you have a bond priced at \(1,000 with an annual interest of \)80, you can find the nominal interest rate using the formula:

• Nominal Interest Rate = (Annual Interest / Bond Price) * 100

Plugging the numbers into this formula, you calculate it as \( (80 / 1000) \times 100 \) which equals 8%.
This is a basic approach, showcasing what the nominal yields are before diving deeper into inflation adjustments.

Real Interest Rate

Next, we turn our attention to the real interest rate. This is a vital concept because it accounts for inflation, offering a clearer picture of the actual earnings from an investment. By considering the rise in general price levels, the real interest rate tells us what our investment's purchasing power truly is.

The real interest rate can be calculated simply using the Fisher equation:

• Real Interest Rate = Nominal Interest Rate - Inflation Rate

In the context of our earlier example, where the nominal interest rate is 8% and expected inflation is 5%, the real interest rate comes to 8% - 5% = 3%.
This crucial adjustment reveals the actual increase in purchasing power, showing more precisely how much buying capability you gain from your investment.

Inflation

Understanding inflation is key to realizing how it impacts interest rates and investment returns. Inflation is the rate at which the general level of prices for goods and services rises, eroding purchasing power. Essentially, the higher the inflation, the less you can buy with the same amount of money.

When inflation is factored into interest rates, it affects both the nominal and real interest rates. It does this by shrinking the real returns on investments if not accounted for. In the previous example, an inflation rate of 5% signifies that the price level is expected to rise, implying lesser value for money across one year.

To truly grasp what your investments yield, accounting for inflation is indispensable. This allows for a realistic assessment of how much more you can afford once price increases have been factored out. The calculation of real interest rates helps investors make informed decisions by highlighting the effect of inflation on nominal returns.