5. Under what conditions will a discount bond have a negative nominal interest rate? Is it possible for a coupon bond or a perpetuity to have a negative nominal interest rate?(consider the yield to maturity is given as i=(C+F-P)/P relationship when answering the question and for perpetuity you would look at the equation: i_(c)=C/P_(c) that why it can be negative)

##Step 1: Discount Bond Condition for Negative Nominal Interest Rate<br />###A discount bond has a negative nominal interest rate when its purchase price (P) exceeds its face value (F). This is because the yield to maturity for a discount bond is given by $i = \frac{F-P}{P}$. If $P > F$, then $F - P < 0$, resulting in a negative $i$.<br />##Step 2: Coupon Bond Condition for Negative Nominal Interest Rate<br />###A coupon bond can also have a negative nominal interest rate. The yield to maturity for a coupon bond is more complex, but simplifies to $i = \frac{C + F - P}{P}$, where C is the coupon payment. If the combined value of the coupon payments and face value ($C + F$) is less than the purchase price ($P$), then the yield to maturity ($i$) will be negative.<br />##Step 3: Perpetuity Condition for Negative Nominal Interest Rate<br />###A perpetuity can have a negative nominal interest rate. The yield for a perpetuity is given by $i_c = \frac{C}{P_c}$. If the price ($P_c$) is significantly high relative to the coupon payment ($C$), the yield ($i_c$) can become negative. This could occur if investors are willing to pay a premium for a guaranteed stream of income, even if that income is relatively small compared to the initial investment.<br /><br />#