# Interest Rates

The time value of money is a concept that states that cash received today is more valuable than cash received in the future. If a person agrees to receive payment in the future, he foregoes the option of earning interest if he invests that amount of money today.

An interest rate or yield, usually denoted by r, is a rate of return that reflects the connection between cash flows dated at different times.

Assume you currently possess $100. Next, consider depositing this money into a savings account, expecting it to grow to$110 after one year. Intuitively, the compensation required for deferring the consumption of $100 now in favor of receiving$110 in one year is \$10 (equal to 110 minus 100). This compensation is equivalent to a 10% rate of return (calculated as 10 divided by 100).

There are three ways to interpret interest rates:

1. Required rate of return: The minimum return an investor expects to earn to accept an investment.
2. Discount rate: The rate used to discount future cash flows to allow for the time value of money (to determine the present value equivalent of some money to be received sometime in the future). Discount rates and interest rates are used almost interchangeably.
3. Opportunity cost: The value of the best-forgone alternative; the most valuable alternative investors give up when they choose what to do with money.

### Determinants of Interest Rates

Economics postulates that the forces of supply and demand determine interest rates. In this case, the investors (lenders) supply the money, and the borrowers demand money for their consumption.

As such, interest is a reward a borrower pays for using an asset, usually capital, belonging to a lender. It is compensation for the loss or value depreciation occasioned by the use of the asset.

Therefore, an interest rate is composed of a real risk-free interest rate plus a set of four premiums that represent compensation for bearing distinct types of risk:

\text{Interest (r)}=\begin{align} &\text{Real risk-free interest rate}\\&+\text{Inflation Premium}\\&+\text{Default risk premium}\\&+\text{Liquidity premium}\\ &+\text{Maturity premium}\\\end{align}

## The Real Risk-free Interest Rate

The real risk-free interest rate is the single-period interest rate for a completely risk-free security if no inflation is expected. According to economic theory, the real risk-free rate reflects people’s preferences for current compared to real future consumption.

Inflation risk is the loss of purchasing power of money as a result of the increase in prices of consumer goods.

The inflation premium compensates investors for expected inflation. It represents the average inflation rate expected over the maturity of the debt. The risk of a decrease in purchasing power validates the inflation risk premium.

Liquidity refers to the ease with which an investment can be converted into cash without significantly sacrificing market value.

The liquidity premium compensates investors for the risk of loss relative to an investment’s fair value if the investment needs to be converted to cash quickly.

Default risk describes a situation where a borrower may fail to repay borrowed funds as a result of bankruptcy. This might result in significant losses on the side of the lender.

The default risk premium compensates investors for the possibility that the borrower will fail to make a promised payment at the contracted time and in the contracted amount.

The maturity risk premium is the additional return an investor requires for assuming interest rate and reinvestment risk resulting from a longer investment maturity timeline. Maturity risk premium increases with an increase in the maturity timeline. In other words, the longer the maturity timeline of an investment, the higher the maturity risk premium.

### Nominal Risk-free Interest Rate

The nominal risk-free interest rate is defined as the sum of the real risk-free interest rate and the inflation premium. In other words, the nominal risk-free interest rate can be seen as the combination of the real risk-free rate plus an inflation premium, as shown by the following equation:

$$\text{(1+Nominal risk-free rate)=(1+Real risk-free rate )(1+Inflation premium)}$$

The above equation is generally approximated as follows:

$$\text{Nominal risk-free rate=Real risk-free rate+Inflation premium}$$

Most rates quoted on short-term government debts can be taken as nominal risk-free interest rates over the respective maturity.

### Question

Which of the following is most likely an interpretation of interest rate as a benefit foregone when investors spend money on current consumption instead of saving or investing?

A. Discount rate.

B. Opportunity cost.

C. Required rate of return.

Solution

Opportunity cost is a key factor in interpreting interest rates. It refers to the interest foregone when investors opt for an alternate option, such as spending on current consumption instead of saving or investing.

A is incorrect. The discount rate is the interest rate used to discount future cash flows to reach the present value.

C is incorrect. The required rate of return is the minimum rate of return an investor would wish to earn to postpone current consumption.

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