What Is Yield to Maturity?
Yield to maturity (YTM) is the total annualized return an investor earns if a bond is bought today and held until it matures, assuming all coupon payments are made on schedule. It accounts for the coupon income, the purchase price, and any gain or loss between the price paid and the face value received at maturity. This calculator uses the widely taught approximate YTM formula, which gives a fast, close estimate without solving the bond-pricing equation iteratively.
How to Use This Calculator
Enter the bond's face value (the amount repaid at maturity, often $1,000), the current price you would pay, the annual coupon rate as a percentage, and the number of years to maturity. The tool computes the annual coupon payment, the current yield, and the approximate yield to maturity instantly.
The Formula Explained
The approximate YTM is:
$$\text{YTM} = \frac{C + \dfrac{F - P}{n}}{\dfrac{F + P}{2}}$$where \(C\) is the annual coupon dollar amount, \(F\) is face value, \(P\) is price, and \(n\) is years. The numerator combines the coupon income with the average annual capital gain or loss. The denominator is the average of price and face value, a proxy for the capital tied up over the bond's life.
Worked Example
Suppose a bond has a $1,000 face value, sells for $920, pays a 6% annual coupon, and matures in 10 years. The annual coupon is $60.
$$\text{YTM} \approx \frac{60 + \dfrac{1000 - 920}{10}}{\dfrac{1000 + 920}{2}} = \frac{60 + 8}{960} = \frac{68}{960} = 0.07083$$or about 7.08%.
FAQ
How accurate is the approximate formula? It is typically within a few tenths of a percent of the true YTM and is excellent for quick comparisons. The exact YTM requires iterative root-finding.
What is the difference between YTM and current yield? Current yield is just coupon \(\div\) price and ignores any gain or loss at maturity, while YTM includes it.
Why is YTM higher than the coupon rate here? Because the bond trades below face value (at a discount), the investor also gains the price-to-par difference, raising the total return.
