A bond with a coupon rate of 65 maturing in 10 years at a va

A bond with a coupon rate of 6.5%, maturing in 10 years at a value of $1,000 and a current market price of $950 will have a yeild to maturity (using the approximation formula) of

a) between 6% and 6.5%

b) between 6.5% and 7%

c) between 7% and 7.5%

d) between 7.5% and 8%

Solution

Subtract the purchase price ($950) from par ($1000). This results in a discount of $50.

Divide the discount ($50) by the remaining years to maturity (10) of the bond.You arrive at the annualized capital gain ($5)

Add the annualized capital gain ($5) to the yearly interest ($65), to obtain total annualized return ($70)

Divide the annualized return ($70) by the purchase price ($950), to obtain yield \"A\", or 7.368%

Subtract annualized capital gain ($5) from par ($1000), to obtain $995

Divide the annualized return ($70) by the result from the previous step ($995), to obtain yield \"B\", or 7.04%

Average the two yields \"A\" and \"B\", or (7.368%+7.04%)/2. This results in 7.20% yield to maturity

Therefore option is C