A city government wants to raise 3 million by issuing bonds

A city government wants to raise $3 million by issuing bonds. By ballot proposition, the bond\'s coupon interest rate was set at 8% per year with semiannual payments. However, market interest rates have risen to a nominal 9% interest rate. If the bonds mature in 20 years, how much will the city raise from issuing $3M in bonds.

Solution

$2,723,976.23


$3M in bonds 8% rate

PV of $3million face value over 20 years = 3,000,000/(1.045^40) = $515786.10
PV of interest = $120,000 semi-annual payments for 40 periods, at 4.5% interest rate
Look up on reference table

18.40 multiplier

PV of interest = $2,208,190.13
Value = PV of interest + PV of face = $2,723,976.23