# YTM — Yield to Maturity

## Yield to Maturity (Definition) | How to Calculate YTM? | Pros & Cons

Yield to maturity (YTM) is the expected return on a bond that an investor will receive if it is held until the maturity date of the bond. In other words, it refers to the returns that a bond will fetch considering all payments made on time throughout the life of the bond.

Redemption Yield or Book Yield are other terms that are used to mention yield to maturity. It equates the bond’s present value of future cash flows (periodic coupon payments and principal amount at maturity) to the market value of the bond.

It is expressed as an annual rate even though it is a long term bond yield.

It can be calculated for bonds as wells as other long term fixed interest-paying securities gilts. Un current yield, which measures the present value of the bond, whereas the yield to maturity measures the value of the bond at the end of the term of a bond.

### Yield to Maturity Formula

YTM considers the effective yield of the bond, which is compounding.

The below formula focuses on calculating the approximate yield to maturity, whereas calculating the actual YTM will require trial and error by considering different rates in the current value of the bond until price matches the actual market price of the bond. Nowadays, there are computer applications that facilitate easy to calculate YTM of the bond.

Approx Yield to Maturity = [C+ (F-P) / n] / [(F+P) / 2]

Where,

• C = Coupon Payment
• F = Face Value
• P = Price
• n = Years to maturity

In the below formula of the present value of the bond, yield to maturity (r) can be calculated.

Present Value of Bond = [C / ( 1+r )] + [C / ( 1+r )2] . . . . . . [C / ( 1+r ) t ] + [F / ( 1+r ) t ]

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To calculate yield to maturity of a bond, the present value of the bond needs to be known. In this way, yield to maturity (r) can be calculated in reverse with the help of the present value of the bond formula.

### Example of Yield to Maturity

ABC Inc issues a bond with a face value of \$1500, and the discounted price is \$1200. The annual coupon for the bond is 10%, which is \$150 per annum. The bond will mature after 10 years.

• Approx Yield to Maturity = [C+ (F-P) / n] / (F+P) / 2
• = [150 + (\$1500 – \$1200) / 10] / (\$1500 + \$1200) / 2
• = 13.33%

The approximate yield to maturity for the bond is 13.33% which is above the annual coupon rate by 3%.

Using this value as yield to maturity (r), in the present value of the bond formula, would result in the present value to be \$1239.67; this price is somewhat close to the current price of the bond, which is \$1200.

When a bond is purchased at a discounted rate, the present value of the yield to maturity is high. In this example, the present value of the bond is lower than the value calculated by the present value formula, which is \$1239.67. By this, we can confirm that the YTM is above 13.33%

By means of trial and error, the actual YTM, in this case, is 13.81%, which is calculated by adjusting the estimated rate to match the present value of the bond with the price of the bond.

With technological advancement, YTM can be calculated using various computer applications and websites.

• Yield to maturity allows an investor to compare the present value of the bond with other investment options in the market.
• TVM (Time value of money) is taken into consideration while calculating YTM, which helps in better analysis of the investment with regards to a future return.
• It promotes making credible decisions as to whether investing in the bond will fetch good returns as compared to the value of the investment at the current state.

• Yield to maturity (YTM) considers coupon payments will be reinvested, whereas, in reality, the reinvestment rate tends to vary.
• The impact of factors sinking funds, call options, or put options within a bond structure are ignored in the YTM.
• Taxes paid are not accounted in the yield to maturity (YTM) calculations and hence can depict an incorrect image of the reality.
• It does not consider the costs involved in purchasing or selling the bonds.
• The calculation requires a lot of trial and error, which is time-consuming and requires a lot of guesswork with regards to what value can be used to bring the price of the bond and the current value to be in line.

### Important Points

• A bond that is bought at a discount has a higher yield to maturity (YTM) than its current yield since the present value of the bond is lower.
• A premium bond has a lower YTM than its current yield since the present value of the bond is higher.
• It is more reliable than the current yield since it considers the time value of money.
• Yield to call and yield to put are variations to YTM depending on whether the bond is callable or puttable, respectively.

### Conclusion

• Yield to maturity is the rate of return that a bond will fetch the investor if the bond is held until its maturity.
• An investor can estimate whether buying a bond is worth the investment by looking at the yield to maturity for the bond.
• Various factors, including the time value of money, are considered while calculating YTM.
• Yield to maturity (YTM) can be calculated for bonds as well as other long term fixed interest-paying securities. Bond investments can be corporate bonds, municipal bonds, treasury bonds, to name a few.

This has been a guide to what is Yield to Maturity (YTM) and its definition. Here we discuss a formula to calculate yield to maturity of bond with example. You can learn more from the following articles –

Источник: `https://www.wallstreetmojo.com/yield-to-maturity-ytm/`

## Yield to Maturity (YTM) — Overview, Formula, and Importance

Yield to Maturity (YTM) – otherwise referred to as redemption or book yieldYieldYield is defined as an income-only return on investment (it excludes capital gains) calculated by taking dividends, coupons, or net income and dividing them by the value of the investment.

Expressed as an annual percentage, the yield tells investors how much income they will earn each year relative to the cost of their investment.

– is the speculative rate of returnRate of ReturnThe Rate of Return (ROR) is the gain or loss of an investment over a period of time copmared to the initial cost of the investment expressed as a percentage.

This guide teaches the most common formulas or interest rate of a fixed-rate security, such as a bondBondsBonds are fixed-income securities that are issued by corporations and governments to raise capital.

The bond issuer borrows capital from the bondholder and makes fixed payments to them at a fixed (or variable) interest rate for a specified period.. The YTM is the belief or understanding that an investor purchases the security at the current market price and holds it until the security has matured (reached its full value), and that all interest and coupon payments are made in a timely fashion.

### How YTM is Calculated

YTM is typically expressed as an annual percentage rate (APR)Annual Percentage Rate (APR)The Annual Percentage Rate (APR) is the yearly rate of interest that an individual must pay on a loan, or that they receive on a deposit account. Ultimately, APR is a simple percentage term used to express the numerical amount paid by an individual or entity yearly for the privilege of borrowing money.. It is determined through the use of the following formula:

Where:

• C – Interest/coupon payment
• FV – Face valuePar ValuePar Value is the nominal or face value of a bond, or stock, or coupon as indicated on a bond or stock certificate. It is a static value determined at the time of issuance and, un market value, it doesn’t fluctuate on a regular basis. of the security
• PV – Present value/price of the security
• t – How many years it takes the security to reach maturity

The formula’s purpose is to determine the yield of a bond (or other fixed-asset security) according to its most recent market price. The YTM calculation is structured to show – compounding – the effective yield a security should have once it reaches maturity.

It is different from simple yield, which determines the yield a security should have upon maturity, but is dividends and not compounded interestCompound InterestCompound interest refers to interest payments that are made on the sum of the original principal and the previously paid interest.

An easier way to think of compound interest is that is it «interest on interest,» where the amount of the interest payment is changes in each period, rather than being fixed at the original principal amount..

### Approximated YTM

It’s important to understand that the formula above is only useful for an approximated YTM. In order to calculate the true YTM, an analyst or investor must use the trial and error method.

This is done by using a variety of rates that are substituted into the current value slot of the formula.

The true YTM is determined once the price matches that of the security’s actual current market price.

Alternatively, this process can be sped up by utilizing the SOLVER functionExcel SolverExcel Solver is an optimization tool that can be used to determine how the desired outcome can be achieved by changing the assumptions in a model.

It is a type of what-if analysis and is particularly useful when trying to determine the “best” outcome, given a set of more than two assumptions. in Excel, which determines a value conditions that can be set.

This means that an analyst can set the present value (price) of the security and solve for the YTM which acts as the interest rate for the PV calculation.

### Example of a YTM Calculation

To get a better understanding of the YTM formula and how it works, let’s look at an example.

Assume that there is a bond on the market priced at \$850 and that the bond comes with a face value of \$1,000 (a fairly common face value for bonds). On this bond, yearly coupons are \$150. The coupon rateCoupon RateA coupon rate is the amount of annual interest income paid to a bondholder, the face value of the bond. for the bond is 15% and the bond will reach maturity in 7 years.

The formula for determining approximate YTM would look below:

The approximated YTM on the bond is 18.53%.

### Importance of Yield to Maturity

The primary importance of yield to maturity is the fact that it enables investors to draw comparisons between different securities and the returns they can expect from each.

It is critical for determining which securities to add to their portfolios.

It’s also useful in that it also allows the investors to gain some understanding of how changes in market conditions might affect their portfolio because when securities drop in price, yields rise, and vice versa.

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• Fixed Income Fundamentals
• Equity vs Fixed IncomeEquity vs Fixed IncomeEquity vs Fixed Income. Equity and fixed income products are financial instruments that have very important differences every financial analyst should know. Equity investments generally consist of stocks or stock funds, while fixed income securities generally consist of corporate or government bonds.
• Held to Maturity SecuritiesHeld to Maturity SecuritiesHeld to maturity securities are securities that companies purchase and intend to hold until they mature. This is un trading securities or available for sale securities, where companies don't usually hold on to securities until they reach maturity.
• Matrix PricingMatrix PricingMatrix pricing is an estimation technique used to estimate the market price of securities that are not actively traded. Matrix pricing is primarily used in fixed income, to estimate the price of bonds that do not have an active market. The price of the bond is estimated by comparing it to corporate bonds with an active market

Источник: `https://corporatefinanceinstitute.com/resources/knowledge/finance/yield-to-maturity-ytm/`

## Yield to Maturity (YTM)

Home Finance Cost of Capital Yield to Maturity (YTM)

Yield to maturity (YTM) is the annual return that a bond is expected to generate if it is held till its maturity given its coupon rate, payment frequency and current market price.

Yield to maturity is essentially the internal rate of return of a bond i.e. the discount rate at which the present value of a bond’s coupon payments and maturity value is equal to its current market price.

Even though it is not a perfect measure of cost of debt, it is better than the current yield and/or coupon rate. It is why it is an important input in determining a company’s weighted average cost of capital.

Yield to maturity of a bond can be worked out by iteration, linear-interpolation, approximation formula or using spreadsheet functions.

### Iteration method

The iteration method of calculating yield to maturity involves plugging in different discount rate values in the bond price function till the present value of bond cash flows (right-hand side of the following equation) matches the bond price (left-hand side):

 P = c × F × 1 − (1 + r)-t + F r (1 + r)t

Where P is the bond price i.e. the price at which the bond is currently trading, F is the face value of the both (which is also its maturity value i.e. the value which the bond issuer will return to the bondholder at maturity), c is the periodic coupon rate, t is the number of coupon payments till maturity of the bond and r is the periodic yield to maturity.

Annual yield to maturity equals periodic yield to maturity multiplied by number of coupon payments per year:

Annual Yield to Maturity = Periodic Yield to Maturity × No of Coupon Payments

If we know P, c, F, m and n, we can solve for r by trying different values.

### Linear-interpolation method

There is an inverse relationship between bond price and bond yield which means that if price is low, yield must be high and vice versa. We can use this relationship to find yield to maturity using the linear interpolation as follows:

• STEP 1: Check if the bond price is lower than the face value. If yes, yield to maturity must be higher than the coupon rate. If no, yield to maturity is lower than the coupon rate.
• STEP 2: Keeping the result from Step 1 in view, set a low r value rL such that the present value of bond cash flows PVL is higher than the bond price.
• STEP 3: Set a high r value rH such that the present value of bond cash flows PVH is lower than the bond-price.
• STEP 4: Use the following equation to solve for yield to maturity r:
 r = rL + PVL × (rH − rL) PVL − PVH

### Approximation formula

Yield to maturity can also be calculated using the following approximation formula:

 YTM = C + (F − P)/n (F + P)/2

Where C is the annual coupon amount, F is the face value of the bond, P is the current bond price and n is the total number of years till maturity.

Alternatively, we can also use Microsoft Excel YLD function to find yield to maturity.

### Illustrative example

Company D's 10-year bond with par value of \$1,000 and semiannual coupon of 8% is currently trading at \$950.

Find the yield to maturity on the bond.

Company D's bond has a par value of \$1,000; semiannual coupon of \$40 (=8%/2×\$1,000); current market price of \$950, and payment frequency of 2 per year.

We can set-up the bond-price equation with the given data as follows:

 \$950 = 8%/2 × \$1,000 × 1 − (1 + r)-2×10 + \$1,000 r (1 + r)2×10

### Interpolation Method

Let us try the iteration method first:

We know that:

• If yield to maturity is equal to the coupon rate, the bond is trading at par;
• If the yield to maturity is lower than the coupon rate, the bond will be trading above par (which means it is trading at premium); and
• If the yield to maturity is higher than the coupon rate, the bond will be trading below par (which means it trading at discount).

In the example above, price (of \$950) is lower than the par value of \$1,000. This tells us that the yield to maturity must be higher than the coupon rate of 8%. We select an annual discount rate above 8%, say 8.5% (which corresponds to periodic discount rate of 4.25%). At this rate, the present value of bond cash-flows (right-hand side) works out to \$966.76.

Similarly, at annual discount rate of 9%, PV of bond cash flows is \$934.96. From this we follow that we need to focus on discount rates between 8.5% and 9%. The iteration method requires us to keep trying different values till we narrow down on a rate which equates the present value of bond cash flows (right-hand side) to bond price (left-hand side).

### Linear-Interpolation Method

From the iteration calculations so far, we know that at the lower discount rate rL of 8.5%, PVL is \$966.76 and at the higher discount rate rH of 9%, PVH is \$934.96. Plugging these numbers into the linear-interpolation formula gives us an estimated yield to maturity of 8.75%.

 r = 8% + \$966.76 × (9% − 8%) = 8.75% \$966.76 − \$934.96

### Approximation Formula

We know that annual coupon C is \$80, face value F is \$1,000, price P is \$950 and n is 10. Plugging these numbers, we find that approximate yield to maturity is 8.72%.

 YTM = \$80 + (\$1,000 − \$950)/10 = 8.72% (\$1,000 + \$950)/2

### Yield to Maturity using YIELD Function

The method that gives us the most accurate measure of yield to maturity is Microsoft Excel YIELD function. We need to assume the bond issue date and maturity date such that the time to maturity is 10 years.

### Limitation of yield to maturity

Yield to maturity carries the same drawback as the internal rate of return: it assumes that the bond’s coupon payments are reinvested at the yield to maturity which is not normally the case.

If coupons are to be reinvested at lower rates, yield to maturity will be an overstated measure of return on bond (and cost of debt).

In other words, yield to maturity does not address a bond’s reinvestment risk.

Further, yield to maturity is valid only when bond is held till maturity. If the bond is disposed off earlier, it is quite possible that it may fetch a price lower than the face value.

There are many other similar measures used such as yield to call, yield to put, cash flows yield, etc.

by Obaidullah Jan, ACA, CFA and last modified on May 18, 2020
Studying for CFA® Program? Access notes and question bank for CFA® Level 1 authored by me at AlphaBetaPrep.com

Источник: `https://xplaind.com/157707/yield-to-maturity`

## Bond Yield to Maturity (YTM) Calculator

On this page is a bond yield to maturity calculator, to automatically calculate the internal rate of return (IRR) earned on a certain bond. This calculator automatically assumes an investor holds to maturity, reinvests coupons, and all payments and coupons will be paid on time.

The page also includes the approximate yield to maturity formula, and includes a discussion on how to find – or approach – the exact yield to maturity.

### Yield to Maturity Calculator Inputs

• Current Bond Trading Price (\$) — The price the bond trades at today.
• Bond Face Value/Par Value (\$) — The face value of the bond, also known as the par value of the bond.
• Years to Maturity — The numbers of years until bond maturity.

### Bond YTM Calculator Outputs

• Yield to Maturity (%): The converged upon solution for the yield to maturity of the bond (the internal rate of return)
• Yield to Maturity (Estimated) (%): The estimated yield to maturity using the shortcut equation explained below, so you can compare how the quick estimate would compare with the converged solution.
• Current Yield (%): Simple yield based upon current trading price and face value of the bond. See the current yield calculator for more.

### Bond Yield to Maturity Formula

For this particular problem, interestingly, we start with an estimate before building the actual answer. That's right — the actual formula for internal rate of return requires us to converge onto a solution; it doesn't allow us to isolate a variable and solve.

### Estimated Yield to Maturity Formula

However, that doesn't mean we can't estimate and come close. The formula for the approximate yield to maturity on a bond is:

( (Annual Interest Payment) + ( (Face Value — Current Price) / (Years to Maturity) ) )

/

( ( Face Value + Current Price ) / 2 )

Let's solve that for the problem we pose by default in the calculator:

• Current Price: \$920
• Par Value: \$1000
• Years to Maturity: 10
• Annual Coupon Rate: 10%
• Coupon Frequency: 2x a Year

100 + ( ( 1000 — 920 ) / 10)

/

( 1000 + 920 ) / 2

=

100 + 8

/

960

=

11.25%

### What's the Exact Yield to Maturity Formula?

If you've already tested the calculator, you know the actual yield to maturity on our bond is 11.359%.

How did we find that answer?

We calculated the rate an investor would earn reinvesting every coupon payment at the current rate, then determining the present value of those cash flows.  The summation looks this:

Price =

Coupon Payment / ( 1 + rate) 1

+

Coupon Payment / ( 1 + rate) 2

+

Final Coupon Payment + Face Value / ( 1 + rate) n

As discussing this geometric series is a little heavy for a quick post here, let us note: for further reading, try Karl Sigman's notes, hosted with Columbia.

For most purposes, such as quickly estimating a yield to maturity, the approximation formula should suffice. — any advanced valuation should be done procedurally, on a computer, anyway.

The calculator internally uses the secant method to converge upon a solution, and uses an adaptation of a method from Github user ndongo.

### Yield to Maturity of Zero Coupon Bonds

A zero coupon bond is a bond which doesn't pay periodic payments, instead having only a face value (value at maturity) and a present value (current value).  This makes calculating the yield to maturity of a zero coupon bond straight-forward:

Let's take the following bond as an example:

• Current Price: \$600
• Par Value: \$1000
• Years to Maturity: 3
• Annual Coupon Rate: 0%
• Coupon Frequency: 0x a Year

Price =

(Present Value / Face Value) (1/n) — 1 =

(1000 / 600) (1 / 3) — 1=

1.6666… (1/3) — 1 =

18.563%

### Conclusion and Other Financial Basics Calculators

Use the Yield to Maturity as you would use other measures of valuation: a factor in your decision whether to buy or avoid a bond.

You can compare YTM between various debt issues to see which ones would perform best. Note the caveat that YTM though – these calculations assume no missed or delayed payments and reinvesting at the same rate upon coupon payments.

For other calculators in our financial basics series, please see:

Источник: `https://dqydj.com/bond-yield-to-maturity-calculator/`

## Yield to Maturity | Components and Examples of Yield to Maturity

Yield to Maturity(YTM) can be described as total anticipated return which an investor will earn on his/her investments starting from date of investment till the ultimate due date of maturity (generally calculated for bonds, debentures, etc.), YTM is generally confused with annual rate of return which is different from YTM or else YTM can be described as discount rate at which sum of all future cash flows from bond will be equal to bond price.

### Components of Yield to Maturity

For the purpose of calculating Yield to Maturity, we need to have a proper understanding of various terms used in the calculation of Yield To maturity (YTM) as follows :

• Coupon Rate: Rate of Interest which a bond offers during its period of investment.
• Redemption Price: Price or value which will accrue to the investor on the final settlement of bond/ investment.
• Issue Price: Initial price at which bond/ Investment is sold by Government/Corporates
• Face Value: Par Value of Bond which neither includes any premium nor offers any discount.
• Yield: Yield can be said as the total amount of return an investor earns or can be said as the return earned on his/her Investment.

Formula #1

YTM =  [n√ (Face Value/ Current Price)n] – 1

Where,

• YTM: Yield to maturity
• n: Number of years to maturity
• Current Price: Bond’s today’s market price
• Face Value: Bond’s par value

Formula #2

YTM = [C + (F-P/n)] / [(F+P)/2]

Where,

• C: Coupon Rate
• F: Face Value (Issue Price)
• P: Market Price of Bond

Formula #3

YTM = [Coupon  + Prorated Discount] / [(Redemption Price + Purchase Price) /2 ]

Let’s take an example to understand the calculation in a better manner.

### Yield to Maturity Formula- Example #1

Calculate the yield to maturity of a bond with the help of following given information:

Solution:

Yield to Maturity is calculated using the formula given below

YTM = [C + ((F – P) / n)] / [(F + P)/2]

• YTM = [13 + (\$100 – \$95 / 6)] / [(\$100 + \$95 )/2]
• YTM = 14.19%

### Yield to Maturity Formula- Example #2

Consider a market bond issued in the market having a bond period of 5 years and an interest coupon rate of 9%. Consider the issue price of Bond at \$ 90, and redemption value be \$ 105.

Calculate the post-tax Yield to Maturity for the investor where the rate of normal Income tax can be assumed at 30% and capital gains are taxed at 10%.

You are required to calculate post-tax yield to maturity.

Solution:

Coupon is calculated as

• Coupon = 0.09 * (1 – 0.30)
• Coupon = 6.30%

Post Tax Redemption Price is calculated as

• Post Tax Redemption Price = \$105 – (1 – 0.10)
• Post Tax Redemption Price = \$104

Yield to Maturity is calculated using the formula given below

YTM =[Coupon  + Prorated Discount] /[(Redemption Price + Purchase Price)/2]

• YTM = [6.30 + (\$13.50 / 5) / [(\$104 + \$90) / 2]
• YTM =  9.08%

## Bond Yield to Maturity Calculator for Comparing Bonds

Yield to maturity measures the internal rate of return you would receive if you held a bond until its maturity date.

To better understand what yield to maturity is, it's important that you have a basic understanding of what bonds are, how they work, and how they are bought and sold.

### What Are Bonds?

Basically, bonds are IOU's issued by a government entity or corporation, which promise to pay you interest on a sum of money borrowed from you — along with the promise to repay the sum of money borrowed at the end of the loan (referred to as the maturity date).

When a government entity or corporation issues bonds (looking to borrow money), the bonds have a stated par value, a stated maturity date, and a stated coupon rate.

### What is Par Value?

The par value (also referred to as the «face value») is the amount the issuer (borrower) promises to pay at the end of the loan period. Typically bonds are issued with par values of \$1,000 and can be purchased for close to their par value on the day they are issued.

### What is Maturity Date?

The maturity date is the date the issuer promises to pay the holder of the bond an amount equal to the par value. Bonds can have maturity dates that range anywhere from 1 day up to 30 years or more.

Generally, the longer out the maturity date, the higher the interest rate the bond will pay. That's because longer maturities expose the bondholder to more risk than bonds with shorter maturities.

### What is Coupon Rate?

The coupon rate is the annual interest rate the issuer will pay on the amount borrowed.

For example, if a bond has a par value of \$1,000 and a coupon rate of 8%, then you will receive annual coupon (interest) payments of \$80 (1000 X .08 = \$80) until the bond's maturity date.

Most bonds make coupon payments semi-annually, so you would ly receive a \$40 coupon payment two times each year.

### What Makes Bond Yield Comparisons Difficult?

What makes comparing bond yields difficult, is that bonds are often bought and sold in between their maturity dates — with the prices of the bonds constantly changing due to changing interest rates and the demand for borrowing money.

In other words, you could buy a newly issued \$1,000 bond today at close to face value, but a month from now the bond might be selling for more or less than what you paid for it.

Generally, if interest rates rise, the prices of bonds fall. And if interest rates fall, the prices of bonds rise. If you're not sure why prices and rates move in opposite directions, please visit the Bond Value Calculator Learn tab for a simple explanation.

In any case, the important thing to realize is that bonds are rarely bought and sold at par value.

This means that if you are looking to invest in bonds, you will ly be purchasing bonds at prices that are higher or lower than their par value. And it's this price-to-par-value variance that makes it difficult to compare yields on bonds with different maturities, prices, and coupon rates.

If you were to purchase a bond at a par value of \$1,000 and held it until maturity, the yield would be roughly equal to the annual coupon rate. However, if you purchase a \$1,000 bond for \$900 (purchased at a discount) with a coupon rate of 6%, how would you know how the actual yield will compare to a \$1,000 bond selling for \$1,100 (purchased at a premium), but that has a coupon rate of 7%?

### Enter the Yield to Maturity Calculation for Comparing Bonds

Yield to maturity is a rather complex return on investment calculation that accounts for both coupon payments and the gain or loss of principal that occurs when bonds are purchased for less than or greater than the par value. But in your case, all you need to do is to enter four variables for each bond, and the yield to maturity calculator will do all of the complex calculations for you.

Please keep in mind that while the yield to maturity calculator can help you compare total returns on bonds, it cannot predict the future.

Bonds, while considered to be safer than equities (stocks), do carry a risk that the issuer may default on the repayment. Of course, this risk is less when it comes to U.S. government bonds and Municipal bonds, and more when it comes to corporate bonds. And as with all types of investments, the greater the risk, the higher the expected return on investment.

Источник: `https://www.free-online-calculator-use.com/yield-to-maturity-calculator.html`