Question

The price of a ten-year semi-annual pay bond with a par value of $1,000 and a 7 percent annual coupon and yield to maturity of 8.25 percent is closest to:

Answer 1

The coupon payment is computed as follows:

= 7% / 2 x $ 1,000 (Since the payments are semi annually, hence divided by 2)

= $ 35

The YTM will be as follows:

= 8.25% / 2 (Since the payments are semi annually, hence divided by 2)

= 4.125% or 0.04125

N will be as follows:

= 10 x 2 (Since the payments are semi annually, hence multiplied by 2)

= 20

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

= $ 35 x [ [ (1 - 1 / (1 + 0.04125)²⁰ ] / 0.04125 ] + $ 1,000 / 1.04125²⁰

= $ 35 x 13.44113095 + $ 445.5533483

= $ 915.99 Approximately

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