Question

A $5,000 corporate bond pays $100 quarterly, and has six years to maturity. If this bond is selling for $5,500.76 what is the interest rate that the market has for this bond?

Answer 1

Face value = 5000

quarterly payment =100

maturity = 6 years = 6*4 = 24 quarters

Present value of the bond = 5500.76

Let market interest rate per quarter = I%, then

5500.76 = 100*(P/A, I%, 24) + 5000*(P/F,i%,24)

Using trail and error method

At I = 0.5%, value of expression 100*(P/A, I%, 24) + 5000*(P/F,i%,24) = 6692.2149

At I = 0.75%, value of expression 100*(P/A, I%, 24) + 5000*(P/F,i%,24) = 6368.0716

At I = 1%, value of expression 100*(P/A, I%, 24) + 5000*(P/F,i%,24) = 6062.169

At I = 1.5%, value of expression 100*(P/A, I%, 24) + 5000*(P/F,i%,24) = 5500.760

So quarterly market interest rate = 1.5%

Nominal market interest rate per year = 1.5%* 4 = 6%