Case 1
- Face value
- 1000
- Coupon rate
- 5%
- Market price
- 925.61
- Years to maturity
- 10
- Coupon payments per year
- 2
6.00%
Open with these valuesYield to Maturity Calculator
6.00%
Result: 6.00 %Yield to maturity is the one rate at which every future payment, discounted back, adds up to today's price. Pay below face value and it comes out above the coupon rate; pay above face value and it comes out below. There is no closed formula, so it is found by search — this calculator halves the interval 200 times.
Worked examples
Case 2
- Face value
- 1000
- Coupon rate
- 5%
- Market price
- 1000
- Years to maturity
- 10
- Coupon payments per year
- 2
5.00%
Open with these valuesCase 3
- Face value
- 1000
- Coupon rate
- 0%
- Market price
- 610.27
- Years to maturity
- 10
- Coupon payments per year
- 2
5.00%
Open with these valuesHow it's calculated
y solves Price = C × [1 − (1 + y)⁻ⁿ] ÷ y + Face ÷ (1 + y)ⁿ
- StepEnter the price you pay, not the face value — the yield is measured against it.
- StepSet the payments per year; they split the coupon and compound the yield.
- StepThe calculator searches for the rate whose discounted cash flows equal that price.
- ResultRead the annual yield, assuming you hold the bond to maturity.
What this number means
It assumes every coupon is reinvested
Holding to maturity is the loud assumption; the quiet one is that each coupon goes back to work at the same yield until the end. Rates move, so your realised return can differ, and that reinvestment risk is why the figure is a benchmark rather than a promise.
Annualised the way the market quotes it
The coupon rate and the result are annual rates; internally both are divided by the payments per year. The yield shown is therefore nominal and compounded per period, which is the market convention.
Found by search, not by formula
There is no closed algebraic solution, so the rate is bracketed between −50 % and 200 % and that interval is halved 200 times. What comes out is the exact root to machine precision for the price you enter.
Commonly misread
Yield to maturity is what I will actually earn.
It holds only if you hold the bond to maturity and reinvest every coupon at the same rate. Neither is guaranteed.
Current yield and yield to maturity measure the same thing.
Current yield is only the annual coupon divided by the price, so it counts income alone. Yield to maturity adds the gain or loss to par and the time left.
Enter the face value in the price field.
Enter the price you actually pay; the yield is measured against it. Pay exactly face value and the yield equals the coupon rate, 5.00 in the example.
Reference table
| Face, coupon, price, years, payments | Position | Yield to maturity |
|---|---|---|
| 1000, 5, 800, 10, 2 | Deep discount | 7.93 |
| 1000, 5, 900, 10, 2 | Discount | 6.37 |
| 1000, 5, 950, 10, 2 | Discount | 5.66 |
| 1000, 5, 1000, 10, 2 | At par, yield equals coupon | 5.00 |
| 1000, 5, 1100, 10, 2 | Premium | 3.79 |
| 1000, 5, 1200, 10, 2 | Deep premium | 2.70 |
Questions
What is yield to maturity?
Yield to maturity is the annual rate of return you earn if you buy a bond at today's price and hold it to maturity, collecting every coupon and the face value at the end. It is the bond's internal rate of return: the discount rate that equates all its cash flows with its price. Because it covers both coupon income and the gain or loss to par, it is the most complete common yield measure.
How is yield to maturity calculated?
It is the rate y that solves Price = C × [1 − (1 + y)⁻ⁿ] ÷ y + Face ÷ (1 + y)ⁿ. There is no neat algebraic solution, so it is found numerically — this calculator brackets the rate between −50 % and 200 % and halves that interval 200 times. A 1000 bond with a 5 % coupon priced at 925.61 over 10 years, paid semi-annually, yields about 6 %.
How is it different from current yield?
Current yield is just the annual coupon divided by the price, so it measures income only. Yield to maturity adds the capital gain or loss you realise because the bond is repaid at face value, and accounts for the time left. For a discount bond it is higher than the current yield, for a premium bond lower.
Why is the yield above or below the coupon rate?
It comes down to the price you pay. Buy below face value and the yield is above the coupon rate, because you also gain when the bond repays at par; buy above face value and the yield is below it, because you take a loss at maturity. Pay exactly face value and yield and coupon rate are the same number.
What does it assume about reinvesting the coupons?
The measure assumes every coupon is reinvested at the same yield until the bond matures. Rates move, so in practice you may reinvest at higher or lower rates and your realised return can differ. That reinvestment risk is why yield to maturity is a benchmark rather than a promise.
Sources and last check
Information, not financial advice.