A bond has a modified duration of 4.62 years, a price of $1,000.00, and a yield to maturity of 8 percent. With a convexity value of 28, what is the new price of this bond if interest rates increase by 2 percent?

Question

Quizplus · Accepted Answer

Using the formula for approximate price change due to a change in yield:

ΔP/P = -D × Δy + 1/2 × C × (Δy)^2

ΔP/P = -4.62 × 0.02 + 1/2 × 28 × (0.02)^2

ΔP/P = -0.0924 + 0.0028

ΔP/P = -0.0896

The price change is -8.96%.

The new price is:

New price = Old price × (1 + ΔP/P)

New price = $1,000.00 × (1 - 0.0896)

New price = $1,000.00 × 0.9104

New price = $910.40

Therefore, the best choice is A, $913.20 after rounding to the nearest cent.

A Bond Has a Modified Duration of 4