Question

A municipality needs funding for upcoming infrastructure (water and sewer line) repair or replacement. They issue a series of $1,000, 6% semiannual, 10-year bonds. The bonds are initially sold at a discount for $960.

If you buy a bond and sell it for $850 immediately following the 8^th interest payment, what is your effective annual rate of return?

Answer 1

PV (purchase price) = -960; PMT (semi-annual coupons received) = coupon rate*par value/2 = (6%*1,000)/2 = 30; FV (selling price) = 850; N (number of coupons received) = 8, solve for RATE.

Semi-annual rate = 1.78%

So, effective annual rate = ((1+ semi-annual rate)^2) -1 = ((1+1.78%)^2) -1 = 3.59%

(Note: From the question, it is not clear whether 6% is the annual or semi-annual rate. If it is assumed to be the semi-annual rate then in the solution shown above, PMT will be 60 and effective annual rate will be 10.36%.)