After purchasing a zero-coupon bond for $945 (its face value is $1,000), news arrives that interest rates on savings accounts at banks have risen to 7%. As a result of the change in interest rates, the price of this bond will:
A) rise by $10.42.
B) fall by $10.42.
C) fall by $66.12.
D) rise by $66.12.

Question

Quizplus · Accepted Answer

Zero-coupon bonds are sold at a discount to their face value and pay no interest, so their prices are highly sensitive to changes in interest rates. When interest rates rise, the present value of future cash flows decreases, which causes prices to fall. In this case, the increase in the interest rate from 6% to 7% will cause the price of the bond to fall by $10.42, calculated as follows:

PV = FV/(1 + r)n 
PV = $1,000/(1 + 0.07)n 
PV = $869.56

Loss = $945 - $869.56 = $75.44 
Loss per year = $75.44/7 = $10.42 (rounded to the nearest cent)

After Purchasing a Zero-Coupon Bond for $945 (Its Face Value