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A $1000 face value coupon bond has a 10% coupon rate, a maturity of 4 years, and a price of $950.

Calculate the present value of the bond when the interest rate is 12%. Must the yield to maturity be above or below 12%, and why?

I got the PV value to be 939.25 but I dont know how to answer the second part of the question regarding yield to maturity. Also what does the interest rate mentioned in this question reflect & how does it differ from YTM?

The reasoning behind your answer would be greatly appreciated.

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    This is suspiciously like a homework question in a course on accounting or finance or business. – Dilip Sarwate Jul 9 '18 at 2:25
  • Aren't the present value and the price the same thing? – DJohnM Jul 9 '18 at 4:32
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    This is not an accounting question, so I don't believe it should be closed. Also homework is not off-topic per se, particularly in this case where there is a specific issue the OP is asking about, not just the answer which has been attempted. – Grade 'Eh' Bacon Jul 9 '18 at 15:13
  • Agreed. The question, however, seems pretty familiar, and might be closed as duplicate. PV, FV, YTM, are important to understand when investing in any bond. – JoeTaxpayer Jul 11 '18 at 12:10
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Must the yield to maturity be above or below 12%, and why?

Bond price is inversely related to yield (the lower the price of a bond, the higher the yield).

So since the PV of a bond at a 12% interest rate is lower than the given price, the actual yield must be lower than 12% in order to raise the price to $950 (you'd have to use trial-and-error to calculate the actual yield).

Also what does the interest rate mentioned in this question reflect & how does it differ from YTM?

The interest rate in the question represents the return you expect from reinvesting the coupon payments. It is arbitrary in this case. The YTM is the interest rate that gives you a PV (price) equal to the market price.

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