1

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?

idknuttin
  • 2,475

1 Answers1

1

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 $\frac{F}{(1+r)^2}\cdot (1+r)^2=F$

callculus42
  • 30,550
  • In class I leanred it as $Value Of Bond = \frac{Face Value}{(1 + Interest Rate)^n}$ so this is wrong beause it doesn't make sense correct? So if I want to calculate how much money I will have after one year if I buy a bond with face value $$1000$ and an interest rate of 5% I would solve the equation $1000=\frac{F}{1 + 0.05}$ and get the answer $$1005$ which makes sense correct? – idknuttin Feb 14 '16 at 19:34
  • 1
    If $ F=$ 1000$ is the face value then you are correct. – callculus42 Feb 14 '16 at 20:12
  • When I was looking up definitions for face value I was finding that the face value is the amount the holder of the bond (the person who bought the bond) will receive at maturity? If I say a bond has face value 100 USD does that mean that is how much I am going to receive at maturity or how much I paid for the bond? – idknuttin Feb 16 '16 at 17:52