# The Relation of Interest Rate & Yield to Maturity

Some bond-related terms are used as synonyms, which can make investment jargon confusing to a new bond investor. The yield to maturity and the interest rate used to discount cash flows to be received by a bondholder are two terms representing the same number in the bond pricing formula, but they have different economic meanings.

### Tip

While yield to maturity is a measure of the total return a bond offers, an interest rate is simply the percentage return offered on an annual basis.

## The Bond Pricing Formula

The bond pricing formula calculates a bond’s price by discounting cash flows that a bondholder receives by an interest rate. Discounting refers to reducing the future cash flow by an amount that reflects the interest earned over time: The higher the interest rate, the lower the present value of the future cash flows and the lower the bond price, which is the sum of the discounted future cash flows. Cash flows consist of coupon payments – the interest paid by the corporation each year, plus the final return to the bondholder of the principal borrowed by the corporation.

## Initial Interest Rates and Bond Prices

When a coupon-paying bond is first issued by a corporation, the coupon rate is often set very close to the return required by investors for a security possessing risk characteristics of the bond being issued. The implication is that the bond will initially be priced close to or at par, which is commonly $1,000. Assume that investors require a 5 percent rate of return. The corporation then issues a group of bonds each priced at $1,000, agrees to pay coupons – or interest – of 5 percent each year; when the bond matures, it pays back the $1,000 in principal that was initially borrowed from the investors.

## When Interest Rates Change

Bonds are also called fixed-income securities because the coupons paid by the corporation issuing a bond do not change over time. However, the economy and interest rate environment do change, and then the return that investors require changes. If the general level of interest rates increase from 5 percent, and investors now demand 6 percent, investors will not pay $1,000 for a 5 percent coupon bond trading in the secondary market.

This is because it still pays the same fixed coupon of each year (5 percent of the par value). To earn 6 percent, a smaller investment – a lower bond price -- is necessary, because bond prices and interest rates are inversely related.

## Yield to Maturity Defined

A bond’s yield to maturity accounts for the price that is paid for a bond as well as the coupons and final principal payment a bondholder receives when the bond matures. The yield to maturity is the yield that you would earn if you held the bond to maturity and were able to reinvest the coupon payments at that same rate. It is the same number used in the bond pricing formula to discount future cash flows.

Rather than using it to find a bond’s price, the bond price is given as the price trading in the market, and the yield to maturity is found as the number that makes the bond price equal to the sum of the discounted cash flows.

References

Writer Bio

Kathryn Christopher has been writing about investments for more than 20 years. Her work has appeared in the "Journal of Alternative Investments" and numerous other academic and industry publications. She works at Wiggin Financial Planning, teaches for UMASSOnline from South Florida, and holds a PhD in finance from the University of Massachusetts.