# Learn How to Calculate Bond Value - Tutorial

## Calculate Bond Price - Definition, Formula and Example

#### Definition :

Bond price is nothing but the sum paid to buy a bond which has an inverse relationship with interest rates. When interest rates increase, the prices fall and when interest rates fall, the prices get increased. It can be priced at a premium, discount, or at par.

#### Formula : #### Example :

Calculate the price of a bond with a par value of \$1,000 to be paid in ten years, a coupon rate of 10%, and a required yield of 12%.

##### Given,

Coupon Payment C = 10% Face Value F = 1000 Interest rate r = 12% Years t = 20

##### To Find,

Annual B0 Semi Annual B0

##### Solution:
###### Step 1:

Since the coupon payments are semi-annual, divide the coupon rate in half. The coupon rate is the percentage off the bond's par value. First multiply the face value with the coupon payment, C = (10 x 1000) / 100 = 100 r = 12 /100 = 0.12

###### Step 2:

Now, substitute the values in the annual B0 formula, Annual B0 = 100 x ( ( 1-(1 / ( 1 + 0.12 )20 ) ) / 0.12 ) + 1000 / (1+0.12)20 = 100 x ( ( 1-(1 / 9.6463 ) ) / 0.12 ) + 1000 / 9.6463 = 100 x ((1 - 0.1037) / 0.12) + 103.6667 = 100 x 7.4692 + 103.66667 = 850.611

###### Step 3:

Substitute the given values in the semiannual B0 formula, Semi Annual B0 = 100/2 x ((1-(1 / (1+(0.12/2))40)) /(0.12/2))+1000 / (1+(0.12/2))40 = 50 x (1-(1/10.2857)) / 0.06 + 1000 / 10.2857 = 50 x (1-0.0972) / 0.06) + 97.22223 = 752.3333 + 97.22223 = 849.537