Questions: How are investors in zero-coupon bonds compensated for making such an investment? Such bonds are purchased at a discount, below their face value.

The answer is the last one: Such bonds are purchased at a discount, below their face value.

Explanation for each option:

1. Such bonds are purchased at their face value and sold at a premium on a later date.
   This is incorrect. Zero-coupon bonds are not typically purchased at face value and sold at a premium. Instead, they are bought at a discount and mature at face value.

2. Such bonds make regular interest payments.
   This is incorrect. Zero-coupon bonds do not make regular interest payments. Instead, they accumulate interest, which is paid out at maturity.

3. Such bonds have a lower face value as compared to other bonds of similar term.
   This is incorrect. The face value of zero-coupon bonds is not necessarily lower than other bonds. The key characteristic is that they are sold at a discount to their face value.

4. Such bonds are purchased at a discount, below their face value.
   This is correct. Investors in zero-coupon bonds are compensated by purchasing the bonds at a price lower than their face value, and they receive the full face value at maturity, which includes the interest that has accrued over the life of the bond.

In summary, zero-coupon bonds are purchased at a discount and do not make regular interest payments, with the investor receiving the face value at maturity.