Question

What is the current price of a $1,000 par value, 8% coupon bond that pays interest semi-annually if the bond matures in 7 years and has a yield-to-maturity of 12%?

A.$814.1

B.$1,058.33

C.$817.45

D.$469.75

Answer 1

The market value is computed as shown below:

The coupon payment is computed as follows:

= 8% / 2 x $ 1,000 (Since the payments are semi annually, hence divided by 2)

= $ 40

The YTM will be as follows:

= 12% / 2 (Since the payments are semi annually, hence divided by 2)

= 6% or 0.06

N will be as follows:

= 7 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 14

So, the price of the bond is computed as follows:

Bonds Price = Coupon payment x [ [ (1 - 1 / (1 + r)ⁿ ] / r ] + Par value / (1 + r)ⁿ

= $ 40 x [ [ (1 - 1 / (1 + 0.06)¹⁴ ] / 0.06 ] + $ 1,000 / 1.06¹⁴

= $ 40 x 9.294983927 + $ 442.3009644

= $ 814.10 Approximately

So, the correct answer is option A.

Feel free to ask in case of any query relating to this question