Question

A municipal bond pays 6.7% interest compounded semiannually on its face value of $2,700. The interest is paid at the end of every half-year period. Fifteen years from now the face value of $2,700 will be returned. The current market interest rate for municipal bonds is 6.1% compounded semiannually. How much should you pay for the bond?

Answer 1

price of bond is present value of all interest payments and future face value at the going market rate
6-month interest= 2700*0.0335 = 90.45
price = 90.45(v+v^2+v^3+...v^30) +2700*v^30
v= 1/1+i = 1/1.0305
i is half of annual rate of 6.1
v is present value of 1 dollar after 6 months
sum of v+v^2+v^3+...v^30 is sum of geometric series
= v*(1-v^30)/(1-v) = 19.474
price = 90.45*19.474 + 2700*v^30 = 2857.74