### Relationship between bond prices and interest rates (video) | Khan Academy

Question: I am confused about the cause/effect relationship between inflation and interest rates. Many economic talking heads claim that. In the United States, interest rates are decided by the Federal Reserve. The Fed meets The Phillips Curve relates the inverse relationship between the two. Why bond prices move inversely to changes in interest rate.

For example, when interest rates on mortgages go up, fewer people can afford to buy homes. That tends to dampen the housing market, which in turn can affect the economy. When the Fed raises its target interest rate, other interest rates and bond yields typically rise as well.

New bonds paying higher interest rates mean existing bonds with lower rates are less valuable. Prices of existing bonds fall. An overheated economy can lead to inflation, and investors begin to worry that the Fed may have to raise interest rates, which would hurt bond prices even though yields are higher.

When rates are dropping, bonds issued today will typically pay a lower interest rate than similar bonds issued when rates were higher. Those older bonds with higher yields become more valuable to investors, who are willing to pay a higher price to get that greater income stream. As a result, prices for existing bonds with higher interest rates tend to rise. Three years later, she wants to sell the bond. That may or may not be good for bonds.

Bond prices may go up. However, a slowing economy also increases the chance that some borrowers may default on their bonds. Also, when interest rates fall, some bond issuers may redeem existing debt and issue new bonds at a lower interest rate, just as you might refinance a mortgage.

If you plan to reinvest any of your bond income, it may be a challenge to generate the same amount of income without adjusting your investment strategy. Under normal conditions, short-term interest rates may feel the effects of any Fed action almost immediately, but longer-term bonds likely will see the greatest price changes.

Also, a bond mutual fund may be affected somewhat differently than an individual bond. Your financial professional may do something similar if you hold individual bonds. Interest rate cycles tend to occur over months and even years.

## Relationship between bond prices and interest rates

Also, the relationship between interest rates, inflation, and bond prices is complex, and can be affected by factors other than the ones outlined here. Your bond investments need to be tailored to your individual financial goals, and take into account your other investments. A financial professional can help you design your portfolio to accommodate changing economic circumstances.

Now, the day that this, let's say this is today that we're talking about the bond is issued, and you look at that and you say, you know what? Now, let's say that the moment after you buy that bond, just to make things a little bit Obviously, interest rates don't move this quickly, but let's say the moment after you buy that bond, or maybe to be a little bit more realistic, let's say the very next day, interest rates go up.

If interest rates go up, let me do this in a new color. Obviously for something less risky, you would expect less interest. Interest rates have gone up. Now, let's say you need cash and you come to me and you say, "Hey, Sal, are you willing to buy "this certificate off of me?

I'll actually do the math with a simpler bond than one that pays coupons right after this, but I just want to give the intuitive sense. Or you could just essentially say that the bond would be trading at a discount to par. Bond would trade at a discount, at a discount to par. Now, let's say the opposite happens. Let's say that interest rates go down. Let's say that we're in a situation where interest rates, interest rates go down.

So how much could you sell this bond for? I'm not being precise with the math. I really just want to give you the gist of it. So now, I would pay more than par. Or, you would say that this bond is trading at a premium, a premium to par.

### What’s the Relationship Between Inflation and Interest Rates? | PBS NewsHour

So at least in the gut sense, when interest rates went up, people expect more from the bond. This bond isn't giving more, so the price will go down. Likewise, if interest rates go down, this bond is getting more than what people's expectations are, so people are willing to pay more for that bond.

Now let's actually do it with an actual, let's actually do the math to figure out the actual price that someone, a rational person would be willing to pay for a bond given what happens to interest rates.

And to do this, I'm going to do what's called a zero-coupon bond. I'm going to show you zero-coupon bond. Actually, the math is much simpler on this because you don't have to do it for all of the different coupons. You just have to look at the final payment. There is no coupon. So if I were to draw a payout diagram, it would just look like this.

This is one year. This is two years. Now let's say on day one, interest rates for a company like company A, this is company A's bonds, so this is starting off, so day one, day one. The way to think about it is let's P in this I'm going to do a little bit of math now, but hopefully it won't be too bad. Let's say P is the price that someone is willing to pay for a bond. Let me just be very clear here. If you do the math here, you get P times 1.

So what is this number right here?