Question

A municipality needs funding for upcoming infrastructure (water and sewer line) repair or replacement. They issue a series of $1,000, 6% semiannual, 13-year bonds. The bonds are initially sold at a discount for $940.

If you buy a bond and sell it for $860 immediately following the 16^th interest payment, what is your effective annual rate of return?

Answer 1

Coupon payment = 6% / 2 * 1000 = 30 per semiannual period

Let semi annual return be i%, then

940 = 30*(P/A,i%,16) + 860*(P/F,i%,16)

Dividing by 10

94 = 3*(P/A,i%,16) + 86*(P/F,i%,16)

using trail and error method

When i = 2%, value of 3*(P/A,i%,16) + 86*(P/F,i%,16) = 3*13.577709 + 86*0.728446 = 103.379467

When i = 3%, value of 3*(P/A,i%,16) + 86*(P/F,i%,16) = 3*12.561102 + 86*0.623167 = 91.275662

using interpolation

i = 2% + (103.379467-94) /(103.379467-91.275662)*(3%-2%)

i = 2% + 0.77% = 2.77%

Effective annual rate of return = (1 + 0.0277)^2 -1

= (1.0277)^2 -1

= 0.05616 ~ 5.62%