A $20,000 municipal bond is offered for sale at $18,000. The bond interest rate is 6 percent per year payable semiannually. The bond will mature and be redeemed at face value 5 years from now. If you purchase the bond, the first premium you will receive is 6 months from today. You have decided that you will invest $18,000 in the bond if your effective semi-annual yield is at least 4 percent. What effective semi-annual rate will this investment yield?

For this calculation we need to use the Effective Annual Yield Formula.

EY = (1 + r/n) ^n - 1

Where:

EY = Effective annual yield r = coupon rate n = number o periods the coupon rate is compounded per year

Plugging the amounts into the formula we obtain:

EY = (1 + 0.06/2) ^2 - 1

EY = 0.062

EY = 6.2%

To obtain the effective semi-annual yield, we simply divide the effective annual yield by two:

= 0.062/2

=0.031

Effective semi-annual yield = 3.1%

In this case, we would not invest in the bond because the effective semi-annual yield does not reach the required 4%.