Final answer:
The security that is likely to have the greatest increase in market value when interest rates decline is long-term bonds.
Step-by-step explanation:
The security that is likely to have the greatest increase in market value when interest rates decline is C. long-term bonds. When interest rates decrease, the value of existing bonds with higher fixed interest rates becomes more attractive compared to newly issued bonds with lower interest rates. This increased demand for higher-yielding bonds causes their prices to rise, resulting in a greater increase in market value for long-term bonds.
For example, let's say you have two bonds, one with a maturity of one year (short-term bond) and another with a maturity of ten years (long-term bond). If interest rates decline, the long-term bond with a higher fixed interest rate will see a larger increase in market value compared to the short-term bond with a lower fixed interest rate.