When you invest in a company's stock, you own a piece of that company. Your fortunes rise and fall with its profits. Fixed income is different. Instead of buying ownership, you're essentially lending money. In return, the borrower promises to pay you back with interest over a set period.

The most common type of fixed-income security is a bond. When you buy a bond, you're lending money to a government or a corporation. In exchange for your loan, the issuer agrees to make regular interest payments, called coupon payments, for a specific amount of time. At the end of that time, when the bond matures, the issuer repays the original amount of the loan, known as the principal or face value.

There are many kinds of bonds. Governments issue Treasury bonds (T-bonds), notes, and bills to fund public spending. Corporations issue corporate bonds to finance operations or expansion. Municipalities issue municipal bonds to build things like schools and highways.

A bond's price isn't always its face value. Bonds are traded on the open market, just like stocks, so their prices can fluctuate. The price of a bond is the present value of all its future cash flows, which includes all the future coupon payments and the final principal repayment.

Let's break that down. The idea of present value is that money today is worth more than the same amount of money in the future because of its potential earning capacity. To find a bond's price, we discount its future payments back to what they're worth today. The discount rate we use is the bond's yield to maturity (YTM).

In this formula:

• $P$ is the price of the bond.
• $C$ is the periodic coupon payment.
• $y$ is the yield to maturity (per period).
• $F$ is the face value of the bond.
• $T$ is the number of periods until maturity.

Yield is the total return you can expect to receive if you hold the bond until it matures. It's expressed as an annual percentage. If you buy a bond for $1,000 and it pays $50 in interest per year, its current yield is 5%.

Bond prices and interest rates have an inverse relationship. When prevailing interest rates in the market go up, the prices of existing bonds go down. When interest rates fall, existing bond prices rise. It works like a seesaw.

Why does this happen? Imagine you buy a bond for $1,000 that pays a 5% coupon ($50 per year). A year later, the central bank raises interest rates, and newly issued bonds with the same risk profile are now paying 6%. Your 5% bond is suddenly less attractive. To sell it, you'd have to lower the price to a point where its yield matches the new 6% market rate. Conversely, if interest rates fell to 4%, your 5% bond would be a hot commodity, and you could sell it for more than its face value.

This relationship is a fundamental principle of the fixed-income market. Understanding it is key to navigating bond investments.