# Bonds: Understanding Investment Performance

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• 0:01 A Bond
• 1:01 Interest and Yield
• 2:46 Calculating Interest Payments
• 3:48 How Much Is the Bond Worth?
• 4:42 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In this video lesson, you will learn how to calculate the worth of a bond over time. Learn how interest payments are calculated. See just how much money can be earned from keeping a bond over time.

## A Bond

Sarah just found out that her dad had bought her a government bond ten years ago. What exactly is a bond? A bond can be described as a loan to be repaid at a future time with interest. What Sarah's dad did in purchasing a government bond was to lend the government some of his money. The government promises to pay back this money at a future date with interest.

Because Sarah's dad bought this bond as a gift to Sarah, the bond and the money is now hers, and she can ask the government to pay her back now or she can continue to wait and let the bond earn interest. The bond that Sarah's dad purchased had a face value or par value of \$1,000 with an interest rate of 5%. Her dad only paid \$900 to purchase this bond ten years ago. Note that this is just an example and does not represent a real government bond that was issued.

## Interest and Yield

When we talk about bonds, there are two terms that you will hear. You will hear people talk about the yield, or the actual interest earned on a bond. This yield is based on the amount you actually paid for the bond. The other term is interest, or the stated interest of the bond. This is the interest that is listed on the bond itself. So, for Sarah's bond, her interest is 5%. What about her yield? To calculate her yield, we need to use this formula:

The par value, or face value, of the bond is \$1,000. The interest is 5%, or 0.05. The price paid for the bond is \$900. Plugging these numbers into the formula we get yield = 0.05 * 1000 / 900 = 0.0555, or 5.55%. So, Sarah's yield is 5.55% instead of the stated 5%. This is because her dad paid less than the face value for the bond. The yield will equal the interest if Sarah's dad had paid the par value for the bond, if he had paid \$1,000 for the \$1,000 bond.

This face value is what the bond was worth when Sarah's dad bought it. Each year that Sarah keeps this bond through, she earns the stated interest on this bond.

## Calculating Interest Payments

To calculate how much interest is earned each year by this bond, we take the par value or face value of the bond and multiply it by the stated interest. So, each year, Sarah's bond earns 0.05 * 1000 = \$50. Depending on the payment schedule of the bond, this \$50 a year could be paid out in two semiannual payments or one annual payment. Usually, it's the two semiannual payments or every six months. So, every six months, Sarah would get paid \$25 in interest.

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