What is yield to maturity (YTM)?

YTM is the single constant annual interest rate that, when used to discount all future coupon payments and the par repayment, exactly equals the bond's current market price. It is the internal rate of return (IRR) of buying the bond today and holding it to maturity. Because the formula has no closed-form inverse, this calculator solves for YTM using Newton-Raphson iteration with a bisection fallback — typically converging in under 20 steps.

How is bond price calculated from a given YTM?

The standard formula is: P = C * [1 - (1+y)^(-n)] / y + FV * (1+y)^(-n), where C is the coupon per period (annual coupon / payments per year), y is the periodic YTM (annual YTM / payments per year), n is the total number of coupon periods, and FV is the face value. The first term is the present value of all coupons (an annuity) and the second term is the present value of the face repayment.

What is the difference between current yield and YTM?

Current yield is simply the annual coupon divided by the current market price. It ignores both the time value of money and any capital gain or loss from buying the bond at a discount or premium to par. YTM accounts for all future cash flows and their timing, making it the better measure of total return. For a par bond the two are equal; for a discount bond YTM exceeds current yield; for a premium bond YTM is lower than current yield.

What is modified duration and why does it matter?

Modified duration (ModD) measures how sensitive a bond's price is to a small change in yield. Specifically, the percentage price change is approximately equal to -ModD times the change in yield (in decimal form). A bond with modified duration 7 will lose about 7% in price if yields rise 1% (100 basis points). It equals Macaulay duration divided by (1 + y), where y is the periodic yield. Investors use it to compare interest-rate risk across bonds with different maturities and coupons.

What is convexity and when does it matter?

Convexity measures the curvature of the price-yield relationship. A straight line (duration alone) underestimates price gains when yields fall and overestimates price losses when yields rise. Adding the convexity term gives a better approximation: dP/P ≈ -ModD * dy + 0.5 * Cx * dy^2. Convexity is always positive for plain vanilla bonds, so bonds with higher convexity outperform lower-convexity bonds of the same duration when yields move significantly.

What is DV01 (dollar value of a basis point)?

DV01 (also called PVBP — price value of a basis point) is the dollar change in a bond's price for a one-basis-point (0.01%) move in yield. It equals ModD times price times 0.0001. Traders use DV01 to hedge interest-rate risk precisely. For example, if a bond has DV01 of $75, a 10 bp yield increase costs $750 in market value per bond.

Bond Yield Calculator

A bond yield calculator that handles both directions of fixed-income arithmetic: give it a market price and it returns the yield to maturity (YTM); give it a YTM and it prices the bond. Either way you also get Macaulay duration, modified duration, convexity, and DV01 — the four numbers that every fixed-income investor needs to understand interest-rate risk. A full coupon cash-flow schedule and a yield-sensitivity table round out the toolkit. Everything runs in your browser; no data is sent anywhere.

How it works

Bond pricing

A fixed-rate bond pays a regular coupon and returns the face (par) value at maturity. Its fair price is the sum of the present values of all those cash flows, discounted at the yield to maturity y (per period):

P = C * [1 - (1+y)^(-n)] / y + FV * (1+y)^(-n)

where C is the coupon per period (annual coupon divided by payments per year), y is the periodic YTM (annual YTM divided by payments per year), n is the total number of coupon periods (years times payments per year), and FV is the face value. The first term is the present value of the coupon stream (an ordinary annuity); the second is the present value of the par repayment.

Solving for YTM

When price is known, YTM has no closed-form solution — it is the root of f(y) = P(y) - market_price = 0. This calculator uses Newton-Raphson iteration seeded with the classic YTM approximation y ≈ (annual coupon + (FV - price) / years) / ((FV + price) / 2), switching to bisection if Newton overshoots. Convergence to eight decimal places typically takes fewer than 20 iterations across all realistic market prices.

Duration and convexity

Macaulay duration is the weighted average time to receive the bond’s cash flows, where each weight is that cash flow’s share of the total present value. It tells you, in years, when you “effectively” get your money back.

Modified duration equals Macaulay duration divided by (1 + y). It gives the percentage price change per unit change in yield: dP/P ≈ -ModD * dy.

Convexity accounts for the curvature of the price-yield relationship, improving the approximation for large yield moves: dP/P ≈ -ModD * dy + 0.5 * Cx * dy^2.

DV01 (dollar value of 01, also called PVBP) is ModD * P * 0.0001 — the dollar price change for a one-basis-point move in yield.

Worked example

Consider a $1,000 par, 5% annual coupon, 10-year bond paying semi-annually, currently trading at $950:

Semi-annual coupon C = 1000 times 0.05 / 2 = $25
Periods n = 10 times 2 = 20
Solving f(y) = 0 gives periodic y ≈ 0.02732, so annual YTM ≈ 5.464%
Current yield = 50 / 950 = 5.26% (lower than YTM because of the pull-to-par capital gain as the discount narrows to zero)
Macaulay duration ≈ 7.99 years, Modified duration ≈ 7.78 years
DV01 ≈ $0.738 per basis point

The sensitivity table confirms: if yields rise 100 bp, the approximated price falls by roughly $73.80 (minus the convexity offset), landing around $876.

Market Price	YTM	Current Yield	Mod. Duration	DV01
$950 (discount)	5.46%	5.26%	7.78 yrs	$0.74
$1,000 (par)	5.00%	5.00%	7.79 yrs	$0.78
$1,050 (premium)	4.56%	4.76%	7.80 yrs	$0.82
$900 (deep discount)	5.97%	5.56%	7.74 yrs	$0.70

Notice that as price falls, YTM rises (inverse relationship) and DV01 falls (you own a smaller dollar amount of sensitivity per bond).