Question

A $5,000 bond with a coupon rate of 5.1​% paid semiannually has eight years to maturity and a yield to maturity of 8.9​%. If interest rates rise and the yield to maturity increases to 9.2​%, what will happen to the price of the​ bond?

Answer 1

The bond's market price will decrease by $72.08 (1.83%) from $3,928.89 to $3,856.81.

Step-by-step explanation:

bond's current market price:

$5,000 / (1 + 4.45%)¹⁶ = $2,491.35

$127.50 x 11.27483 (PV annuity factor, 4.45%, 16 periods) = $1,437.54

current market price = $3,928.89

if interests rise and YTM increases to 9.2%, then new market price:

$5,000 / (1 + 4.6%)¹⁶ = $2,434.80

$127.50 x 11.15305 (PV annuity factor, 4.45%, 16 periods) = $1,422.01

current market price = $3,856.81