if Bond price= the discounted value of all the future income it will generate

then does it mean that the buyer of the bond earn nothing?
Because he in fact need to pay the discounted value of the future income(interest) which is said to be earned by him when buying the bond.
THEN HOW CAN HE EARN THE INTEREST FROM BUYING BONDS?
if not, what can he earn?
I really don't understand,please explain in details,thx!

And is the bond price=face value?

When an investor buys a bond, they are essentially lending money to the issuer (such as a government or corporation) in exchange for regular interest payments and the return of the principal amount at a specific maturity date. The bond price represents the discounted value of all the future income the bond will generate, which includes both the interest payments and the repayment of the principal.

The buyer of the bond indeed pays the discounted value upfront, and it might seem like they are not earning anything from buying the bond. However, this is not entirely accurate. The buyer earns interest income over the life of the bond.

To clarify, let's consider an example:

Suppose you buy a $1,000 bond with a maturity period of 10 years, an annual coupon rate of 5%, and a discount rate of 4%. The coupon rate represents the percentage of the bond's face value that will be paid annually as interest income. In this case, the annual interest income would be $50 (5% of $1,000).

So, the bond will pay you $50 in interest income each year for 10 years, totaling $500 ($50 * 10). Additionally, at the end of the 10-year period, you will receive the principal amount of $1,000.

Now, let's discuss how the buyer earns interest from buying bonds:

1. Coupon Payments: The primary way a bond buyer earns interest is through coupon payments. As mentioned earlier, the bond pays a fixed percentage (coupon rate) of its face value (principal) as interest income. In the example above, the bond pays $50 annually as interest income, which adds to the earnings of the buyer.

2. Capital Appreciation: In some cases, bond prices can rise after they are issued, which can allow investors to sell the bond at a higher price. If the bond appreciates in value during its life and you sell it before maturity, you can earn additional income.

3. Reinvestment of Coupon Payments: When you receive coupon payments, you can reinvest that income into other investments to earn additional returns. By compounding the interest earned from coupon payments, you can increase your overall earnings.

4. Reduced Risk: Bonds are generally considered less risky than other forms of investments, such as stocks. They provide a fixed income stream, which can be attractive to risk-averse investors.

In summary, when a bond buyer purchases a bond, they pay the discounted value upfront but earn interest income through periodic coupon payments, potential capital appreciation, reinvestment of coupon payments, and the reduced risk associated with bond investments.