How does a bonds value change with the interest rate?

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How does a bonds value change with the interest rate?
A bonds value (price) is the discounted value (present value) of the coupon payments and the redemption amount that a bondholder receives
The coupon payments and the redemption amount does not change over the life of the bond,i.e they do not change with the market interest rate. However discounting depends on the interest rate and as interest rates change the discounting factor changes.
We use interest rate to discount the payments. Higher the discount rate , lesser is the Present value / Discounted value
Therefore when the interest rate increases the value of the bond decreases and when the interest rate falls the bond value increases.

Let us explain it with the help of an example:

Let the par /face value/redemption mount be equal to $1,000
Let the coupon rate be 10%
Let the coupon payments be annual
Let the life of the bond be 10 years

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Solution Summary

Explains why bond's value changes with a change in interest rates.

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