Question

Suppose a 10-year, $1,000 bond with an 8.3% coupon rate and semi-annual coupons is trading for a price of $1,034.65. a. What is the bond's yield to maturity (expressed as an APR with semi-annual compounding)? b. If the bond's yield to maturity changes to 9.5% APR, what will the bond's price be?

a. What is the bond's yield to maturity (expressed as an APR with semi-annual compounding)? The bond's yield to maturity is %. (Round to two decimal places.)
b. If the bond's yield to maturity changes to 9.5% APR, what will the bond's price be? The new price for the bond will be $ . (Round to the nearest cent.)

Answer 1

a. The bond's yield to maturity is 7.88% APR with semi-annual compounding. b. The new price for the bond will be $971.62.

Step-by-step explanation:

a. The bond's yield to maturity (expressed as an APR with semi-annual compounding) can be calculated using the formula:

YTM = (C + (F - P)/n) / ((F + P)/2)

Where: C is the coupon payment, F is the face value, P is the bond's price, and n is the number of periods until maturity. In this case, the coupon payment is $41.50 (8.3% of the face value), the face value is $1,000, the bond's price is $1,034.65, and there are 20 periods until maturity. Plugging in these values, the bond's YTM is 7.88% APR with semi-annual compounding.

b. To calculate the new price of the bond when the YTM changes to 9.5% APR, we can use the same formula and plug in the new YTM value. The new price will be $971.62.