While most governments issue fixed coupon bonds with principal paid at maturity, for many government issuers such as the United States, United Kingdom, or India, investors buy and sell individual interest or principal cash flows separated (or stripped) from these instruments as discount bonds. Consider a single principal cash flow payable in 20 years on a Republic of India government bond issued when the YTM is 6.70 percent. For purposes of this simplified example, we use annual compounding, that is, t in Equation 5 is equal to the number of years until the cash flow occurs. 

1. What should an investor expect to pay for this discount bond per INR100 of principal? 

2. If we assume that interest rates remain unchanged, what is the price (PV) of the bond in three years’ time? 

3. Prices also change as interest rates change. Suppose after purchase at t = 0 we observe an immediate drop in the bond price to INR22.68224 per INR100 of principal. What is the implied interest rate on the discount bond? 

4. Now consider a bond issued at negative interest rates. In July 2016, Germany became the first eurozone country to issue 10-year sovereign bonds at a negative yield. If the German government bond annual YTM was −0.05 percent when issued, calculate the present value (PV) of the bond per EUR100 of principal (FV) at the time of issuance. 

5. Six years later, when German inflation reached highs not seen in decades and investors increased their required nominal rate of return, say we observed that the German government bond in question 4 is now trading at a price (PV) of EUR95.72 per EUR100 principal. What is the YTM on this bond?