Question

In April \(2016,\) the nominal interest rate on a one-year Treasury bill was 0.54 percent. From April 2016 to April \(2017,\) the consumer price index rose from 238.9 to \(244.2 .\) If you bought the one-year Treasury bill in April 2016, calculate the real interest rate you earned over the following 12 -month period. Given the results of your calculation, why were investors willing to buy Treasury bills in April \(2016 ?\)

Short answer

First, the real interest rate is calculated by subtracting the inflation rate over the year (approximately \(2.22 \% \)) from the nominal interest rate, resulting in a negative real interest rate. Then, under the assumption of rational investors, despite the negative real rate, investors might have still been willing to buy these Treasury bills due to their relative safety and low risk, compared to other types of investments during this period.

Step-by-step solution

Define Given Information

The nominal interest rate is \(0.54\) percent. The Consumer Price Index (CPI) in April 2016 was \(238.9\) and in April 2017 it rose to \(244.2\). The task is to calculate the real interest rate.

Calculate Inflation Rate

The inflation rate is calculated by the formula: \( \frac{CPI_{new} - CPI_{old}}{CPI_{old}} \times 100\% \). In this case it would be: \( \frac{244.2 - 238.9}{238.9} \times 100\% \).

Convert Nominal Interest to Real Interest

The real interest rate is calculated by substracting the inflation rate from the nominal rate. Use the equation: Real Rate = Nominal Rate - Inflation, substituting the calculated values.

Explanation for Investment

Basing on the calculated real interest rate, deduce the reasons why investors were still willing to buy these Treasury bills.

Key concepts

Nominal Interest Rate

The nominal interest rate represents the percentage increase in money that an investor earns on a financial instrument without adjusting for inflation. In simpler terms, it's the rate advertised by financial institutions on products like savings accounts and Treasury bills. It does not reflect the purchasing power of money.

• For example, if you invest $100 at a nominal interest rate of 0.54%, you would get an additional $0.54 after a year, making your total $100.54.
• This rate is not adjusted for changes in the price level, which means it doesn’t account for inflation.

While the nominal rate gives a basic idea of returns, it is essential to consider the inflation rate for an accurate assessment of the investment's purchasing power over time.

Inflation Rate

The inflation rate measures how much the prices of goods and services increase over time, which indicates a decline in purchasing power. It is crucial when evaluating real returns on investments like Treasury bills. In the provided exercise, the inflation rate is calculated using changes in the CPI between two dates.

• The formula is: \( \text{Inflation Rate} = \frac{\text{CPI}_{\text{new}} - \text{CPI}_{\text{old}}}{\text{CPI}_{\text{old}}} \times 100\% \).
• In this case, it is the difference in the CPI from April 2016 (238.9) to April 2017 (244.2) divided by 238.9, all multiplied by 100 to convert into percentage form.
• This reflects the average increase in price level that impacts an investor's real returns.

Understanding inflation helps investors gauge how much of their purchasing power will be retained after earning interest on their investments.

Treasury Bills

Treasury bills are short-term debt instruments issued by the government to finance its obligations. They are considered low-risk investments because they are backed by the full faith and credit of the government. Investors often turn to Treasury bills for a safe place to park their money temporarily.

• They are sold at a discount and do not pay periodic interest like traditional bonds; instead, investors receive the face value at maturity, and the difference from the purchase price is their interest income.
• Despite often offering low nominal interest rates, their low risk makes them appealing during uncertain economic periods when higher returns might come with significant risk.

The attraction of Treasury bills largely relies on their safety, liquidity, and the role they play in portfolio diversification.

Consumer Price Index (CPI)

The Consumer Price Index (CPI) is a measure that examines the average change over time in the prices paid by urban consumers for a basket of consumer goods and services. It is one of the most used indicators for inflation and reflects the cost of living for consumers.

• A rising CPI indicates increasing inflation, meaning consumers need to spend more money to buy the same goods and services.
• For investors, the CPI is crucial in understanding inflation's impact on purchasing power, as it affects the real returns on investments.

In financial contexts, such as evaluating real interest rates on Treasury bills, the CPI plays a vital role in determining whether investment returns are keeping up with inflation, ensuring investors don't lose purchasing power over time.