Question

An FI purchases at par value a $100,000 Treasury bond paying 10 percent interest with a 7.5 year duration. If interest rates rise by 4 percent, calculate the bond's new value. Recall that Treasury bonds pay interest semiannually. Use the modified duration valuation equation.

Answer 1

The bond's new value is $70,000

Step-by-step explanation:

First calculate the percentage change in the value of the bond

Duration = Percentage change in price / Percentage change in yield

Percentage change in price = Duration x Percentage change in yield

where

Duration = 7.5 years

Percentage change in yield = 4%

Percentage change in price = ?

Placing value sin the formula

Percentage change in price = 7.5 x 4%

Percentage change in price = 0.30

Percentage change in price = 30%

As we know that the value of the bond and the yield rate are inversely proportional to each other, If the yield rate increases the value of the bond decreases due to the discounting factor used in the valuation o the bond.

Hence, the value of the bond is calculated as follow

Value of the bond = Par value of the bond x ( 1 - per centage of change in the price of the bond

Value of the bond = $100,000 x ( 1 - 30% )

Value of the bond = $100,000 x 0.70

Value of the bond = $70,000