### Approximate bond modified duration

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1. Suppose today's 10-year rate is 9 percent. Today's 4-year rate is 7 percent. Estimate the 6-year forward rate in four years if the 10-year rate has a .3 percent liquidity premium.

1. Consider a 30-year corporate bond paying 9 percent semi-annual coupon. The current yield to maturity is 11 percent.
2. Find the modified duration.
3. Refer to part a. If the interest changes by 25 basis points, what is the exact change in price?
4. Refer to part b. If the interest changes by 25 basis points, what is the approximate change in price?

Consider a 30-year corporate bond paying 8 percent semi-annual coupon. The current yield to maturity is 10 percent. Find the approximate bond's modified duration by using changes in the interest rate up and down by 5 basis points.

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