This Bond Yield Calculator estimates the Yield to Maturity (YTM) using the complex approximate formula, allowing users to solve for Coupon Payment, Face Value, Current Price, or Years to Maturity.
Welcome to the **Bond Yield Calculator**. The Yield to Maturity (YTM) is the total return anticipated on a bond if it is held until its maturity date. YTM is an important metric for comparing different fixed-income investments. This tool allows you to solve for the approximate YTM ($Y$), Annual Coupon Payment ($C$), Face Value ($FV$), Current Price ($P$), or Years to Maturity ($T$).
Bond Yield Calculator
Bond Yield Formula
The core approximate relationship for Yield to Maturity (YTM) is:
$$ Y \approx \frac{C + \frac{FV – P}{T}}{\frac{FV + P}{2}} $$
1. Solve for YTM (Y, as a decimal):
$$ Y = \frac{C + (FV – P)/T}{(FV + P)/2} $$
2. Solve for Annual Coupon (C):
$$ C = Y \times \frac{FV + P}{2} – \frac{FV – P}{T} $$
3. Solve for Years to Maturity (T):
$$ T = \frac{FV – P}{Y \times \frac{FV + P}{2} – C} $$
4. Solve for Current Price (P):
$$ P = \frac{FV \times (1 – Y \times T / 2) + C \times T}{1 + Y \times T / 2} $$
Formula Source: Investopedia – Yield to Maturity (YTM)
Variables Explained
- YTM (Y) – Approximate Yield to Maturity: The estimated total return on the bond, annualized. (Output in percentage)
- Coupon (C) – Annual Coupon Payment: The total dollar amount of interest paid per year.
- Face Value (FV) – Par Value: The nominal value paid to the holder at maturity.
- Current Price (P) – The actual market price of the bond today.
- Years (T) – Years to Maturity: The remaining time until the bond matures.
Related Calculators
What is Bond Yield?
Bond Yield, specifically Yield to Maturity (YTM), represents the internal rate of return (IRR) of a bond’s cash flows—the coupons and the principal repayment—assuming the investor holds the bond until maturity and all coupon payments are reinvested at the same rate. It is the most comprehensive measure of a bond’s return.
YTM differs from the simple Coupon Rate (the stated interest rate on the bond) and Current Yield (annual coupon divided by current price). YTM accounts for the time value of money and the capital gains or losses realized if the bond is bought at a discount or premium.
When a bond’s current price ($P$) is less than its face value ($FV$), it is trading at a discount, and the YTM will be greater than the Coupon Rate. Conversely, if $P > FV$, it trades at a premium, and the YTM will be lower than the Coupon Rate.
How to Calculate Current Price (Example)
You want to find the current price ($P$) of a bond with an annual **Coupon Payment** ($C$) of **$60**, a **Face Value** ($FV$) of **$1,000**, **5 Years** ($T$) until maturity, and an expected **YTM** ($Y$) of **7%** (0.07).
- Determine the Missing Variable: Current Price ($P$) is missing.
- Apply Formula: $$ P = \frac{FV \times (1 – Y \times T / 2) + C \times T}{1 + Y \times T / 2} $$
- Substitute Values: $Y \times T / 2 = 0.07 \times 5 / 2 = 0.175$.
- Calculate Numerator: $1000 \times (1 – 0.175) + 60 \times 5 = 1000 \times 0.825 + 300 = 825 + 300 = 1125$.
- Calculate Denominator: $1 + 0.175 = 1.175$.
- Determine Price: $P = 1125 / 1.175 \approx 957.45$. The Current Price is **$957.45**.
Frequently Asked Questions (FAQ)
The true YTM calculation requires finding the interest rate that equates the present value of all future cash flows (coupons and par value) to the current market price, which usually requires iterative methods. The approximate formula uses averages to simplify this process, making it solvable algebraically.
What is the relationship between Price and Yield?Price and Yield have an inverse relationship. When a bond’s price goes up, its yield goes down, and vice versa. This is because the fixed coupon payment represents a smaller percentage return relative to a higher price.
Can the YTM be negative?YTM is typically non-negative. A negative YTM would only occur in extremely rare market conditions where an investor is guaranteed to lose money by holding a bond to maturity. The calculation is typically constrained to be positive as it represents a rate of return.
Does this calculator assume semi-annual payments?The standard approximate YTM formula used here is often simplified for annual payments. For true semi-annual bonds, the inputs $C$ (coupon) and $Y$ (yield) should be divided by 2, and $T$ (time) should be multiplied by 2.