A $500 bond was issued on May 1,2008.It pays quarterly coupons at j₄ = 8% and is redeemable at par on May 1,2023.It was purchased for $X on July 16,2010 to yield j₄ = 12%.What is $X?

Question

Quizplus · Accepted Answer

Step 1: Calculate the number of quarters between May 1,2008 and July 16,2010:
There are 10 quarters between May 1,2008 and July 16,2010.
Step 2: Calculate the number of quarters between July 16,2010 and May 1,2023:
There are 49 quarters between July 16,2010 and May 1,2023.
Step 3: Calculate the future value of the bond:
FV = 500 * (1 + 0.08/4)^(49) = $1,368.17
Step 4: Calculate the present value of the bond:
PV = 50 * (1 - 1/(1 + 0.12/4)^(49)) / (0.12/4) + 1,368.17/(1 + 0.12/4)^(40) = $997.61
Therefore, the purchase price on July 16,2010 to yield 12% is $370.56. The answer is (B).

A $500 Bond Was Issued on May 1,2008