Bond Calculator

What a bond is and what this calculator does

A bond is a loan that an investor makes to a government or company. In return, the issuer pays regular interest, called coupons, and repays the face value at maturity. Bonds trade in the market, so their price changes as interest rates change. This calculator finds the price a bond should sell for, given its coupon, its face value, the years left to maturity and the yield that a buyer requires.

The yield to maturity is the return an investor earns if they buy at the given price, hold to maturity and receive every payment on time. It is the key input because it reflects what the market demands, not the coupon the bond was issued with.

How the price is worked out

The price is the present value of all the future payments. Each coupon is discounted at the yield, and so is the face value received at maturity. The formula is Price = sum of coupon ÷ (1 + y) to the power t, plus face value ÷ (1 + y) to the power n. This calculator assumes annual coupons, which is simpler than the twice-yearly payments many bonds make.

A worked example

A bond with a face value of 1,000, a 5% coupon and ten years to maturity pays 50 a year. If buyers require a 6% yield, the coupons and the repayment are discounted at 6%, and the bond sells for about 926. It sells below face value because its coupon is lower than the yield the market is asking. If the required yield were 4%, the same bond would sell above face value.

The rule to remember: prices and yields move in opposite directions

When yields rise, existing bonds with lower coupons become less attractive, so their prices fall. When yields fall, their prices rise. This is why bonds can lose value even when the issuer pays every coupon on time. The longer the time to maturity, the larger the price change for a given move in yields.

What the calculator does not include

Real bonds often pay coupons twice a year, which changes the timing and the price slightly. Accrued interest between coupon dates is not added. The calculator does not consider credit risk, the chance that the issuer fails to pay, or the liquidity of the bond. Dealer spreads, taxes on interest and any call features that let the issuer repay early are also left out.

Reading the price against the yield

A bond price moves inversely to yield. If market yields rise above a bond's coupon, its price falls below par, and if yields fall, the price rises above par. The calculator shows this relationship for the inputs you choose, which helps explain why bond values fell sharply in periods when interest rates rose quickly.

The price you pay also depends on the time left to maturity. A longer bond is more sensitive to a change in yield than a shorter one with the same coupon. Before buying, check the accrued interest, the fees and the tax treatment, because these change the return you keep.

Using the result

Use the calculator to check whether a quoted price is consistent with the yield you expect, and to see how sensitive a bond is to a change in yields. Test a higher and a lower yield before deciding. The result is an estimate: the actual price will depend on the market at the time of the trade.