Question

# Thunderbolt industrial firm has issued \$1,000 bonds that are guaranteed to pay \$20 semi-annually until the...

Thunderbolt industrial firm has issued \$1,000 bonds that are guaranteed to pay \$20 semi-annually until the bond matures. The bonds mature 20 years from now, at which time the industrial firm will redeem them for \$1,000 plus the final semi-annual interest payment. From the financial pages of your newspaper you learn that the bonds may be purchased today for \$715 each (\$710 for the bond plus a \$5 sales commission). What nominal annual rate of return would you receive if you bought the bond now and held it to maturity 20 years from now?

Question 4 options:

 3.30% 6.60% 4.12% 8.24%

t = 20*2 = 40 semiannual periods

Let the semiannual ROR be i%, then

20*(P/A,i%,40) + 1000*(P/F,i%,40) = 715

Dividing by 5

4*(P/A,i%,40) + 200*(P/F,i%,40) = 143

using trail and error method

When i = 3%, value of 4*(P/A,i%,40) + 200*(P/F,i%,40) = 4*23.114772 + 200*0.306557 = 153.770456

When i = 4%, value of 4*(P/A,i%,40) + 200*(P/F,i%,40) = 4*19.792774 + 200*0.208289 = 120.828904

using interpolation

i = 3% + (153.770456-143) /(153.770456-120.828904)*(4%-3%)

i = 3% + 0.32% = 3.32%

Nominal return = 3.32% *2= 6.64% (Approx) ~ 6.60% (second option)

Minor diff in answer values as calculations are done by hand and upto only 6 decimal places