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I am working on the following problem.

A 10 year bond bearing a $7\%$ coupon rate payable semiannually is bought to yield $5\%$ semiannually. The bond is redeemable at par. If the bond is purchasable at the price of $950$, what is the yield rate?

The coupon rate is higher than the original yield rate, so the price of the current bond is at a premium.

$$PV=1000(1+(3.5\%-2.5\%)a_{\overline{20}\rceil 2.5\%}) \approx 1155.89$$

is the price of the bond before the discount.

If this bond is available at a price of $950$, then I am thinking that the yield rate can be calculated as

$$950(1+j)^{20}=1155.89(1.025)^{20}$$

which gives us

$$j \approx 3.52\%$$

However, the book that I am working on tells me that this value must be $3.86\%$.

I have a feeling that I am not understanding the question correctly. I appreciate your help.

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The bit about being bought to yield 5% semiannually, actually is described as a bond-equivalent yield of 10% p.a. This would mean that the coupon rate of 7% p.a. is less than its yield and so the bond will be priced at a discount ... at 813.07. This bit of information about the 5% semiannual yield is a bit irrelevant ... because the question as I read it says: "If the 7% (semiannual-pay) 10-year bond is priced at 950, what is its yield ?" Of course, the answer is indeed 3.86% semiannual yield, or a bond-equivalent yield of 7.72% p.a. [If you are usuing a business calculator ... N=20, Int=the answer we want, PV=-950, PMT=35 & FV=1000.] Done.

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