# Nominal interest rate and real relationship with bonds

### The Relationship Between Bonds and Interest Rates- Wells Fargo Funds

A nominal interest rate is the interest rate that does not take inflation into account. It is the interest rate that is quoted on bonds and loans. He noted that the real interest rate on government bonds (or the difference between the nominal interest rate and the inflation rate) has also. At first glance, the inverse relationship between interest rates and bond prices Zero coupon bonds are issued at a discount to par value.

So what we've been doing is we've been, at least in the first video, we converted everything to today's dollars. So the actual dollar return in today's dollars is the amount that we got or the net dollar return. And the net dollar return is the amount that we originally invested compounded by the nominal interest rate. And here we're assuming that we're writing it as a decimal. And so this is going to be 0. Or this whole value is going to be 1.

## The Relationship Between Bonds and Interest Rates

And so this is how much we're going to get after a year has passed. And then from that, you want to subtract how much we invested in today's dollars.

Well, we originally invested P dollars a year ago.

And in today's dollars, we just need to grow it by the rate of inflation. So that would be 0.

So this expression right over here is actually the dollar return in today's dollars. It's this value right here that we calculated in the first video.

And to calculate the real return we want the dollar return in today's dollars divided by the investment in today's dollars. And once again, this is the investment in today's dollars. 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.

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

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? Let's get a calculator out.

**Relationship between bond prices and interest rates - Finance & Capital Markets - Khan Academy**

Let's get the calculator out. If we have 1, divided by 1. Now, what happens if the interest rate goes up, let's say, the very next day?

## Relationship between bond prices and interest rates

And I'm not going to be very specific. I'm going to assume it's always two years out. It's one day less, but that's not going to change the math dramatically. Let's say it's the very next second that interest rates were to go up. Let's say second one, so it doesn't affect our math in any dramatic way.

Subtract the annual inflation rate from the nominal interest rate. For example, if a bond has a 5 percent nominal interest rate and the inflation rate is 3 percent, the real interest rate equals 2 percent Significance For investors, the difference between a nominal and real interest rate is of major importance.

Suppose the inflation rate ranges around 3 percent. If you sell the bonds after a few years, the purchasing power of the dollars you are paid will have fallen by perhaps 20 percent. The inflation premium offsets the loss resulting from inflation. Nominal Rate and Compound Interest The interest on most bonds is paid directly to investors.

However, some income investments, like bank certificates of deposit, accrue interest, thereby increasing the principal value of the security. The added money then earns more interest, called compound interest. The term "nominal interest" is sometimes applied to the base interest rate for such investments, and the compound interest rate is referred to as the actual interest rate.