What change in interest rate is required to make call option, Finance Basics

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What change in interest rate is required to make call option

Problem

I. A bond has a modified duration of 4.1 years and trades at 101.80. There is a call option on the bond with a strike price of 102.5. What change in interest rates is required to make the call option just at the money?

II. You purchased a bond at par and now it trades at 101.00. The yield to maturity has decreased 31 bp since you bought the bond. What was its modified duration when you bought it?

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