Final answer:
The present value of a bond increases when the interest rate decreases. This occurs because future cash flows from the bond are worth more when discounted at a lower prevailing market interest rate.
Step-by-step explanation:
All else held constant, the present value of a bond increases when the interest rate decreases. This is because the present value of future cash flows from the bond is calculated by discounting them back to the present using the prevailing market interest rate. When the interest rate falls, the discounted value of these future cash flows increases, making the bond more valuable. Conversely, if interest rates were to rise, the present value of the bond would decrease because the future cash flows would be discounted at a higher rate, making them less valuable in today's dollars. The effect of the maturity period on the present value of a bond is less straightforward and depends on the shape of the yield curve, but in general, a bond's present value is influenced more significantly by changes in interest rates.