# Explain bond valuation with the following example:Calculate the market price of a \$1,000 face value bond with a 14% coupon rate with 30 years until maturity.  Current market rate is 9%.

The fair market price of a bond is given by the sum of the present value of all the cash inflows over the life of the bond.

P = C/(1+d) + C/(1+d)^2 +... C/(1+d)^n + M/(1+d)^n where C is the annual interest received, d is the discount rate, M is the maturity value and n is the life of the bond.

The series C/(1+d) + C/(1+d)^2 +... C/(1+d)^n can be evaluated as C*(1 - (1+d)^n)/d

This process is illustrated by calculating the value of the bond described in the problem.

Here, the interest payments are at a rate of 14% or \$140, the maturity value is \$1000 and the discount rate is 9%. This gives:

P = 140/(1.09) + 140/(1.09)^2 +... + 140/(1.09)^30 + 1000/(1.09)^30

=> 140(1 - (1.09)^-30)/(0.09) + 1000/(1.09)^30

=> 1438.31 + 75.37

=> 1513.68

The value of the bond is \$1513.68

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