Question

If the real interest rate is 1.8% per year, the inflation premium is 3.1% per year, the liquidity premium is 0.3% per year, the maturity premium is 0.4% per year, and the default premium is 2.6% per year, what is the annual risk-free interest rate?

Answer 1

The annual risk-free interest rate is calculated by adding the real interest rate to all applicable premiums, which in this case results in an 8.2% annual risk-free rate when the premiums are added to the given real rate of 1.8%.

Step-by-step explanation:

To calculate the annual risk-free interest rate, we need to consider the real interest rate as the starting point and then add the various premiums that generally compose the nominal interest rate in a fully functioning capital market. The real interest rate reflects the underlying, inflation-adjusted return on an investment without any other types of risk.

In this case, the real interest rate is given as 1.8%. We will add the premiums to this rate to find the risk-free rate:

• Inflation premium: 3.1%
• Liquidity premium: 0.3%
• Maturity premium: 0.4%
• Default premium: 2.6%

To calculate the nominal interest rate, which reflects the risk-free rate in this case, we add these premiums to the real interest rate:

1.8% (real interest rate) + 3.1% (inflation premium) + 0.3% (liquidity premium) + 0.4% (maturity premium) + 2.6% (default premium) = 8.2%

Therefore, the annual risk-free interest rate is 8.2%.