A bond with 10 years until maturity,an 8% coupon,and an 8% yield to maturity increased in price to $1,107.83 yesterday.What apparently happened to interest rates?

Question

Quizplus · Accepted Answer

When the bond's price increased, the yield to maturity must have decreased. Since the coupon rate is 8% and the yield to maturity is also 8%, it means that the bond was trading at par (i.e., its original price). But when it increased in price to $1,107.83, it means that the yield to maturity must have decreased below 8% (because bond prices and yields have an inverse relationship). To calculate the approximate decrease in yield, we can use the bond pricing formula:

PV = C(1 - 1/(1+r)^n)/r + F/(1+r)^n

where PV is the bond price, C is the coupon payment, r is the yield to maturity, n is the number of periods (years), and F is the face value of the bond.

If we plug in the values given, we get:

$1,107.83 = $80(1 - 1/(1+r)^10)/r + $1,000/(1+r)^10

Solving for r using a financial calculator or Excel, we get:

r = 6.46%

This is 1.54% lower than the original yield of 8%, so the answer is D, Rates decreased by 1.5%.

A Bond with 10 Years Until Maturity,an 8% Coupon,and an 8