Current yield and annual interest

Annual interest is the coupon times par

How much interest does a bond pay you each year? A bond is a loan you make, and the borrower pays you interest for using your money. The coupon is the interest rate printed on the bond. Par is the 1,000 dollars you get back at maturity, the end date.

Annual interest is the coupon times par. Use 1,000 dollars for par unless the question says otherwise. Say Sam owns a 5 percent bond. 5 percent of 1,000 is 50 dollars a year.

Most bonds pay interest twice a year, six months apart. So Sam gets two checks of 25 dollars. If Sam owns ten of these bonds, multiply by ten. He gets 500 dollars a year, or 250 every six months.

The common mistake is giving one 25 dollar check when the question asks for the year. Read whether it wants a year or six months. Annual interest is the coupon times par. The price you paid for the bond doesn't change it.

A bond quote is a percent of par

What does it mean when a bond is quoted at 95? Bond prices are quoted as a percent of par. Par is the 1,000 dollars you get back at maturity. So 95 means 95 percent of 1,000. That's a price of 950 dollars.

Picture a price tag that says 102. That's 102 percent of par, or 1,020 dollars. It's above par, so it's a premium. Quotes can have fractions. 96 and a half means 96.5 percent of par, which is 965 dollars.

The quick way is to multiply the quote by 10. That gives you the price in dollars. A common slip is reading 105 as 1,005 dollars. It's 105 percent of par, which is 1,050 dollars.

A bond quote is a percent of par. Multiply it by 10 to get the price in dollars.

Current yield is interest divided by today's price

What return do you get on the money you actually pay for a bond? That's current yield: the yearly interest divided by today's price. Annual interest is the coupon times par, the 1,000 dollars paid back at maturity. A 5 percent bond pays 50 dollars a year, whatever its price.

Say Jen buys that bond at 95. Quotes are a percent of par, so she pays 950 dollars. Divide the 50 dollars of interest by her 950 dollar price. That's 5.26 percent, her current yield.

She earns more than 5 percent because she paid less than par. A discount pushes current yield above the coupon, and a premium pushes it below. The common mistake is dividing by par. 50 over 1,000 is just the 5 percent coupon again. Divide by the price instead.

Current yield is the yearly interest divided by today's price, not by par.

Worked example: current yield of a 5% bond at 95

1. A 5 percent bond is quoted at 95. What's its current yield? Current yield is annual interest divided by price.
2. Step one, the annual interest. That's the coupon times par, so 5 percent of 1,000 is 50 dollars.
3. Step two, the price. A quote is a percent of par, so 95 means 950 dollars.
4. Step three, divide the interest by the price. 50 over 950 is 5.26 percent.
5. Step four, check it. The bond is below par, a discount, so its current yield should beat the 5 percent coupon. 5.26 beats 5.

Common mistakes

divide by the price, not par

You divided by par. Current yield uses the price you pay today. Take an 8 percent bond at 80. Dividing 80 dollars by 1,000 just gives back the 8 percent coupon. Divide by the 800 dollar price instead. That's 10 percent. Current yield is interest divided by today's price.