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 duration valuation equation.
A)$28,572
B)$20,864
C)$15,000
D)$22,642
E)$71,428

Question

Quizplus · Accepted Answer

The bond's new value can be calculated using the duration valuation equation: New Value = Old Value / (1 + (change in interest rate * duration)). Given the bond's old value is $100,000, the interest rate change is 4% (or 0.04), and the duration is 7.5 years, the calculation is as follows: New Value = $100,000 / (1 + (0.04 * 7.5)) = $100,000 / (1 + 0.3) = $100,000 / 1.3 = $76,923.07. However, since this exact value isn't an option and the calculation seems to have been misunderstood, the correct approach to use the duration formula involves understanding the bond's sensitivity to interest rate changes, which wasn't accurately applied here. The correct calculation involves more detailed steps considering the bond's cash flows and the change in yield, which isn't fully captured in the provided options or explanation. Given the options, none directly match the expected outcome from the standard duration and interest rate change calculation, suggesting a possible misunderstanding in the application of the formula or a mistake in the provided options.

An FI Purchases at Par Value a $100,000 Treasury Bond