# Yield to Maturity Calculator

Created by Wei Bin Loo
Reviewed by Dominik Czernia, PhD and Jack Bowater
Based on research by
Forbes SM, Hatem JJ, Paul C. Yield-to-Maturity and the Reinvestment of Coupon Payments Journal of economics and Finance Education (2008)
Last updated: Jan 15, 2023

The yield-to-maturity calculator (YTM calculator) is a handy tool for finding the rate of return that an investor can expect on a bond. As this metric is one of the most significant factors that can impact the bond price, it is essential for an investor to fully understand the YTM definition.

We have written this article to help you understand the meaning of YTM, how to calculate it using the YTM equation, and the factors that cause YTM to rise and fall. We will also demonstrate some examples to help you understand the concept more thoroughly.

## What is YTM? The YTM meaning

Before discussing the YTM calculation, we must first understand what a bond is. A bond is a financial instrument that governments and companies issue to get debt funding from the public.

If you hold a bond, you are entitled to collect a fixed set of cash payments. In practice, this means that until the bond matures, you receive regular interest earnings or coupon payments. When you arrive at the end of the bond's lifespan or maturity date, you get not only the last interest payment but also recover the face value of the bond, that is, the bond's principal.

As bonds are a particular type of investment, their precise evaluation is crucial in the eyes of investors. The most important aspect of the assessment is whether money is made or lost on the investment. That is, what is the return on the financial transaction? And this is what YTM represents and what can be found with this yield-to-maturity calculator.

You can think of the YTM as the rate of return on a bond. If you hold the bond to maturity after buying it in the market and can reinvest the coupons at the YTM, the YTM will be the internal rate of return (IRR) of your bond investments.

Now that we know the YTM definition let's take a look at some examples to understand the YTM equation and its calculation.

## Yield to maturity calculator: how to find YTM and the YTM formula

The YTM formula needs five inputs:

• bond price - Price of the bond;
• face value - Face value of the bond;
• coupon rate - Annual coupon rate;
• frequency - Number of times the coupon is distributed in a year; and
• n - Years to maturity.

Let's take Bond A issued by Company Alpha, which has the following data, as an example of how to find YTM:

• Bond price: $980 • Face value:$1,000
• Annual coupon rate: 5%
• Coupon Frequency: Annual
• Years to maturity: 10 years
1. Calculate the bond price

The bond price is the money an investor has to pay to acquire the bond. It can be found on most financial data websites. The bond price of Bond A is $980. See our bond price calculator for more on how to calculate bond prices. 2. Determine the face value The face value is equivalent to the principal of the bond. For our example, face value =$1,000.

3. Determine the annual coupon rate and the coupon frequency

The coupon rate is the annual interest you will receive by investing in the bond, and frequency is the number of times you will receive it in a year. In the yield-to-maturity calculator, you can choose from six different frequencies, from annual to daily.

In our example, Bond A has a coupon rate of 5% and an annual frequency. This means that the bond will pay $1,000 × 5% =$50 as interest each year.

4. Determine the years to maturity

The n is the number of years from now until the bond matures. The n for Bond A is 10 years.

5. Calculate the bond YTM

The YTM can be seen as the internal rate of return of the bond investment if the investor holds it until it matures and reinvests the coupon at the same interest rate. Hence, the YTM formula involves deducing the YTM r in the equation below:

$\qquad \small {\rm bond\ price} = \sum_{k=1}^{n} \frac{cf}{(1+r)^k},$

where:

cf - Cash flows, i.e., coupons or the principal;
r - YTM; and
n - Years to maturity.

This yield-to-maturity calculation involves complex iteration, and it is nearly impossible to do it by hand. And that's why we have built this calculator for you! We also have a dedicated bond YTM calculator available.

For Bond A, the equation looks like this:

$\footnotesize \qquad \begin{split} 980 &= \frac{\50}{(1+r)^1} + \frac{\50}{(1+r)^2}\\[1em] &\ \ + \frac{\50}{(1+r)^3} + ... + \frac{\50}{(1+r)^9}\\[1em] &\ \ + \frac{\1,050}{(1+r)^{10}} \end{split}$

After performing the estimation, our YTM calculator gives a YTM that is equal to r = 5.26%.

## What does YTM mean and what are the main factors that will affect YTM?

Now that you understand the YTM meaning and how to calculate the YTM, let's explore its economics, i.e., why does YTM rise and fall, and what are the main factors affecting it:

• The most important factor in determining YTM is inflation (see the inflation calculator). When inflation is higher than expected, YTM will rise. This is because investors anticipate that the central banks will increase interest rates to curb and control inflation. Note we haven't included inflation in this bond yield calculator.

• The other important factor is the uncertainty of the market conditions. Investors despise uncertainty in general. The more volatile the market conditions, the more uncertainty investors will face. Due to the higher uncertainty, investors will demand a higher rate of return to compensate for the risks they undertake – check out our risk calculator. This can therefore cause YTM to rise.

## Understanding the yield curve

The yield curve is one of the best instruments to analyze the evolution of YTM. The bond yield curve plots the YTM against time.

For instance, if the yield curve is upward-sloping, the long-term YTM, such as the 10-year YTM, is higher than the short-term YTM, such as the 2-year YTM. On the other hand, if the yield curve is trending downwards, the 10-year YTM will be lower than the 2-year YTM.

## FAQ

### Does bond yield equal to YTM?

Technically, yes. Bond yield will equal YTM if you hold to the bond until its maturity and reinvest at the same rate as the YTM.

### What is a yield curve?

The yield curve is a graph drawn for YTM against time. It shows the evolution of YTM with time. If the yield curve trends upwards, it means that the long-term YTM is greater than the short-term YTM.

### What causes YTM to fall?

There are several factors that can make YTM fall. For instance, the lower the inflation, the lower the YTM. Also, the less volatile the market condition, the lower the YTM.

### Can YTM be negative?

Yes, YTM can be negative. It happens every now and then, even though it is not common. This situation normally happens when inflation is out of control and the market is unstable.

In such a situation, even a negative YTM is still better than storing cash since hyperinflation might happen.

Wei Bin Loo
Face value
$Bond price$
Annual coupon rate
%
Coupon frequency
Annually
Years to maturity
year(s)
Yield to maturity (YTM)
%
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