anonymous
  • anonymous
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?
Mathematics
katieb
  • katieb
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dumbcow
  • dumbcow
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

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