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.
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.
How did we get $25? Well, six months is half a year, so half of $50 is $25. Mathematically, we divided the 50 by 12 to find that the monthly payment is 4.1667. Multiplying this by 6 to find the payment after six months, we get $25.
How Much Is the Bond Worth?
Sarah has had this bond for ten years now. How much is this bond worth now? Well, it still has a face value of $1,000. But it has been earning interest for 10 years. How much interest? We can multiply the interest earned each year by the number of years Sarah has kept this bond. We get $50 * 10 = $500. So, this bond has earned $500 in interest. We can say that after ten years, the bond is worth $1500: $1,000 for the par value and $500 from the interest.
That's pretty cool for Sarah. She wants to hold onto her bond because $50 earned per year for not doing anything other than holding onto a piece of paper representing the bond is not a bad deal.
Let's review what we learned. We learned that a bond can be described as a loan to be repaid at a future time with interest. Its par value is its face value. Its yield is the actual interest earned on a bond, and interest is the stated interest of the bond. To calculate the yield of a bond, we multiply the stated interest by the par value of the bond and then divide by the amount paid for the bond. To calculate how much interest is earned per year, we multiply the stated interest by the par value.
After this lesson, you should be able to:
- Describe what a bond is
- Define par value, yield and interest in terms of bonds
- Explain how to calculate the yield of a bond and its interest earned per year