Why is the yield to maturity different from the coupon rate?

Because the coupon is a percentage of face value, while your return depends on the price you paid. Buy below face value and the difference is an extra gain at redemption, so your yield is above the coupon; buy above it and the opposite.

Which yield should I compare two bonds on?

Yield to maturity, because it counts both the coupons and the redemption amount. Current yield can rank two bonds in the wrong order when one trades at a discount and the other at a premium.

Why does the price fall when yields rise?

A bond you hold pays a fixed coupon. If new bonds pay more, nobody will pay you the old price for the old coupon — the price has to fall until the return to a new buyer matches what is available elsewhere. The longer the remaining maturity, the further it falls.

Does this apply to debt mutual funds?

The same arithmetic drives them, since a debt fund holds bonds, but a fund has no maturity date of its own, charges an expense ratio and is marked to market daily. Treat this as the mechanics behind the fund rather than a model of one.

Bond Yield Calculator

A bond’s coupon rate is a percentage of its face value, not of what you paid for it. This works out the two yields that matter — current yield and yield to maturity — from your own price, and shows what a one percentage point rise in market yields would do to the price.

Check the working

A worked example

A fixed case, for reference.

A ₹1,000 bond paying a 7% coupon twice a year, with five years to run, bought for ₹950.

Each coupon
$\frac{1000 \times 7\%}{2} = 35$
Ten coupons over five years
$35 \times 10 = 350$
Current yield
$\frac{70}{950} = 7.37\%$
Gain at redemption
$1000 - 950 = 50$
Yield to maturity, solved from the price
$\approx 8.24\%$

The coupon rate is 7%, the current yield 7.37%, and the yield to maturity about 8.24%. Three different numbers for one bond — the third is the one that counts the ₹50 you get back at redemption, and the only one worth comparing against another bond.

The formula

P = \sum_{k=1}^{n} \frac{C}{\left(1 + \frac{y}{m}\right)^{k}} + \frac{F}{\left(1 + \frac{y}{m}\right)^{n}}

The price is the present value of every coupon plus the face value, discounted at the yield to maturity.

\text{Current yield} = \frac{F \times c}{P}

Current yield ignores the redemption amount entirely, which is why it differs from the yield to maturity whenever the price is not the face value.

What each symbol means

P: the price you pay
F: face value, repaid at maturity
C: one coupon payment
c: the coupon rate, as a decimal
y: yield to maturity, per year
m: coupon payments per year
n: the total number of coupon payments

What this assumes, and where it stops

Assumptions

Every coupon is paid in full and on time, and the issuer repays the face value at maturity. Credit risk is not modelled.
Coupons are assumed to be reinvested at the yield to maturity, which is what the formula means. If you spend them, or reinvest them at a lower rate, your realised return is lower.
The bond is bought on a coupon date, so no accrued interest is added to the price.
The redemption amount is the face value — no call, no put, no partial redemption.

Limitations

Tax is not modelled. Coupon income and any gain on sale or redemption are taxed differently from each other.
Floating-rate, callable, puttable and convertible bonds do not price this way.
Accrued interest between coupon dates is ignored, so a mid-period purchase will differ from a broker’s figure.
The one-point repricing is a straight-line move in the whole yield curve, which is not how yields actually move.
Nothing here is specific to any bond, and no security is named or assessed.

What this calculator does

Calculates current yield: the annual coupon divided by the price you pay.
Solves for yield to maturity: the rate at which every coupon plus the redemption amount discounts back to that price.
Separates the two sources of return — the coupons, and the gain or loss booked when the bond redeems at face value.
Reprices the bond one percentage point higher, so interest-rate risk is a number rather than a warning.

Common questions

Different questions about the same money. These use the same conventions, so the numbers are comparable.

FD Calculator
Work out what a fixed deposit pays at maturity, and see how much more you get by reinvesting the interest instead of having it paid out.
PPF Calculator
Project a Public Provident Fund balance under the scheme’s own rule — interest on the lowest balance between the 5th and month-end — and see what missing that date costs.
XIRR Calculator
Calculate the annualised return on irregular cashflows — the right measure when money went in and out on different dates.
DCF Calculator
Discount projected future cashflows back to a present value — the core of intrinsic valuation, with its assumptions made explicit.