There is an inverse relationship between bond prices and yields. This inverse re

Question

There is an inverse relationship between bond prices and yields. This inverse relationship will be demonstrated by calculating bond prices to show that interest rates move inversely: if yields rise, then bond prices fall. Bonds will be sold either at a premium or a discount. With this in mind respond to the following question. You currently own a 30 year Treasury Bond at 4% interest, paid semiannually. The market interest rates for like securities rose to 5%. Would your bond sell for a premium or a discount? Why? What would the market value of your bond be? Prove your answer by showing your work.

Explanation / Answer

If market rate is 5% present value / current sell value of bonds can be calculated as follows

=Present value of principle + Present value of all interest payments

= $1000(PVIFA,60,2.5%) +$1000*2% ((PVIF,60,2.5%)

= $1000(PVIF,60,2.5%) +$20 ((PVIFA,60,2.5%)

= $1000 *0.2273 +20(30.9087)

=$227.30 +$618.17

= $845.47

Market value of Bond will be  $845.47

Bond would be sold at discount of $154.53 ($1000- $845.47)

Because rise in interest rate of 1% has fallen the price to  $845.47 because there is an inverse relationship between bond prices and yields. This inverse relationship will be demonstrated by calculating bond prices to show that interest rates move inversely: if yields rise, then bond prices fall. Bonds will be sold either at a premium or a discount.

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