can someone explain how bonds work and how to calculate the value of a bond? I am taking financial mathematics and in class I learned a formula to calculate the value of a bond, $B=\frac{F}{1+r}$ if one payment or if coumpund $B=\frac{F}{(1+r)^n}$ where $B$ is the value of the bond, $F$ is the face value and $r$ is the interest rate and $n$ is the time (matuarity). I have trouble understanding what the face value is? Let's says eomeone buys a bond for $\$1000$ with a return of 5% in one payment paid after one year. If I plug those numbers into the formula I get about $\$952$. But if you buy a bond worth $\$1000$ with 5% return after one payment (1 year) I would think you will get $\$1005$ once the bond matures? Can someone explain how bonds work, the terminology and calculations, but just in simple terms for now. What is the difference between the face value and value of the bond?

The creditor is the owner of the bond. After $n$ years she/he will get $F$ Dollars from the debitor. This F Dollars are the **future value**. To get the present value $F$ Dollars have to be discounted $n$ years. $r$ is the interest rate for riskless investments. And $1+r$ is the discount factor. Therefore the **present (face) value** is

$$PV=\frac{F}{(1+r)^n}$$

If you have a positive interest rate a particular amount of money (F) in present has a higher value than this particular amount of money in the future. To get $F$ in two years you have to invest _only_ $\frac{F}{(1+r)^2}$. After two years you will have $\frac{F}{(1+r)^2}\cdot (1+r)^2=F$