How often must a nominal rate of 18% be compounded in order to yield 18.81% annually?

What Are the Different Interest Rates?

The term “interest rate” is one of the most commonly used phrases in the fixed-income investment lexicon. The different types of interest rates, including real, nominal, effective, and annual, are distinguished by key economic factors, that can help individuals become smarter consumers and shrewder investors.

Key Takeaways

• Different types of interest rates, such as real, nominal, effective, and annual, are set apart by critical economic factors.
• The nominal interest rate, or coupon rate, is the actual price borrowers pay lenders, without accounting for any other economic factors.
• The real interest rate accounts for inflation, giving a more precise reading of a borrower's buying power after the position has been redeemed.
• The effective interest rate includes the impact of compounding, in which a bond might pay interest annually but compounds semiannually, increasing the overall return.

Nominal Interest Rate 

The nominal interest rate is the stated interest rate of a bond or loan, which signifies the actual monetary price borrowers pay lenders to use their money. If the nominal rate on a loan is 5%, borrowers can expect to pay $5 of interest for every $100 loaned to them. This is often referred to as the coupon rate because it was traditionally stamped on the coupons redeemed by bondholders.

Real Interest Rate

The real interest rate is so named, because unlike the nominal rate, it factors inflation into the equation, to give investors a more accurate measure of their buying power, after they redeem their positions. If an annually compounding bond lists a 6% nominal yield and the inflation rate is 4%, then the real rate of interest is actually only 2%.

Special Considerations

It’s feasible for real interest rates to be in negative territory if the inflation rate exceeds the nominal rate of an investment. For example, a bond with a 3% nominal rate will have a real interest rate of -1%, if the inflation rate is 4%. A comparison of real and nominal interest rates can be calculated using this equation:

RR = Nominal Interest Rate  −  Inflation Rate where: RR = Real Rate of Return \begin{aligned} &\text{RR}=\text{Nominal Interest Rate }-\text{ Inflation Rate}\\ &\textbf{where:}\\ &\text{RR = Real Rate of Return}\\ \end{aligned} ​RR=Nominal Interest Rate − Inflation Ratewhere:RR = Real Rate of Return​

Several economic stipulations can be derived from this formula, which lenders, borrowers, and investors may utilize to cultivate more informed financial decisions.

• Typically, when the inflation rates are negative (deflationary), real rates exceed nominal rights. But the opposite is true when inflation rates are positive.
• One theory believes the inflation rate moves in tandem with nominal interest rates over time, meaning that real interest rates become stable over long time periods. Therefore, investors with longer time horizons may be able to more accurately assess their investment returns on an inflation-adjusted basis.

Effective Interest Rate

Investors and borrowers should also be aware of the effective interest rate, which takes the concept of compounding into account. For example, if a bond pays 6% annually and compounds semiannually, an investor who places $1,000 in this bond will receive $30 of interest payments after the first 6 months ($1,000 x .03), and $30.90 of interest after the next six months ($1,030 x .03). In total, this investor receives $60.90 for the year. In this scenario, while the nominal rate is 6%, the effective rate is 6.09%.

Mathematically speaking, the difference between the nominal and effective rates increases with the number of compounding periods within a specific time period.

Forces Behind Interest Rates

Applications

The differences between nominal, real, and effective rates are important when it comes to loans. For example, a loan with frequent compounding periods will be more expensive than one that compounds annually, which is a vital consideration when shopping for mortgages.

Furthermore, a bond that pays just a 1% real interest rate may not adequately grow an investor’s assets over time. Simply put: interest rates effectively reveal the true return that will be posted by a fixed-income investment and the true cost of borrowing for individuals or businesses.

TIPS and Other Alternatives

Investors who seek protection from inflation in the fixed-income arena may elect to consider Treasury Inflation-Protected Securities (TIPS), which pay interest rates that are indexed to inflation. Mutual funds investing in bonds, mortgages, and senior secured loans that pay floating interest rates, also periodically adjust with current rates.

The Bottom Line

When it comes to a bond’s interest rates, shrew investors know to look beyond nominal or coupon rates when considering their overall investment objectives. A qualified financial advisor can help investors navigate interest rates that keep up with inflation.

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