The present value of an expected future payment "falls" as the interest rate increases.
This is based on the idea that the bond is paid at a fixed interest rate. Thus as the interest rate increases, the value of the bond decreases or falls because investors would certainly stay away from such bonds, therefore, making its value reduce or fall.
Similarly, if the interest falls, a bond with a fixed interest rate becomes more attractive to investors.
Hence, in this case, it is concluded that the interest rates determine the value of the bond.
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