Bond price against the market rate

The line is the price of one bond at every market rate on the axis, quoted per 100 of face value the way bonds are quoted. Par is the 100 line, so anything above it costs more than the bond repays at maturity and anything below it costs less.

$$P = \sum_{t=1}^{n} \frac{C}{(1+i)^t} + \frac{F}{(1+i)^n}$$

$C$ is the coupon paid each period, $F$ is the face value repaid at the end, $n$ is the number of periods left and $i$ is the market rate for one period. Coupon and face value are fixed the day the bond is issued. Only $i$ moves, and it sits in the denominator of every term, so raising it shrinks all of them at once. That is the whole reason the curve slopes down. The rate on the axis is a nominal rate for a year, split into the two coupon periods the tool assumes.

The curve is bowed rather than straight. A fall in the market rate lifts the price by a little more than an equal rise takes off it, because discounting divides rather than subtracts. That bow is convexity, and it is why the left of the chart climbs away faster than the right of it drops.

The vertical dashed line sits at the coupon rate and the horizontal dashed line sits at par. They cross at the one point every curve for this coupon passes through, whatever its maturity: when the market rate equals the coupon rate, the bond pays exactly what the market is asking and it prices at 100.

Left of that crossing the market rate is below the coupon, so the bond pays more than a newly issued one, buyers bid it up, and it trades at a premium. Right of the crossing the market rate is above the coupon, the bond pays less than a new one, and it trades at a discount. The two shaded regions are those areas.

Current yield reads the coupon against the price paid rather than against face, so it moves with the price. On the default settings the coupon is 5 percent of face and 5.40 percent of the discounted price. Rate moves are usually quoted in basis points, one hundredth of a percentage point, so a 1 point move on the slider is 100 of them.

Drag the maturity slider and the live curve tips steeper around the par crossing while the fainter fixed curve behind it stays put. A longer maturity means more payments and, more to the point, payments further away, each discounted by the market rate compounded over more periods. A change in that rate has more compounding to act on, so the same move in rates produces a bigger move in price.

The two readings under the chart put a number on it. On the default settings a 1 point rise takes 7.3 percent off the 10 year bond and 2.7 percent off the 3 year one. That sensitivity to rates is what duration measures. Duration is quoted in years because the same present value weights also give the average time until the money arrives, so the two figures sit close together without being the same number. Read the 7.3 as a percentage per point, not as a count of years.

A lower coupon steepens the curve for the same reason: the less of the total that arrives early as coupons, the more of it waits at the far end for maturity, and the further out money sits the harder discounting hits it. Longer means a bigger swing for as long as the bond is priced at or above par, which is the case to learn first. The tool can reach the exception, so it is worth seeing: take the coupon to 1 percent and drag the market rate to the top of the axis, and the reading peaks around 19 years and then eases off, because nearly all of that bond is the single repayment at the end and pushing it further out discounts it away faster than it adds sensitivity. This page is educational material about how the arithmetic works, not financial advice.