Bill de Blasio, the current mayor of New York City, is planning to build a new, expensive library for the city. His term in office ends in 2017 and he will announce the construction of the library to gain some votes from the student population of the City. He wants the library to be built by 2021, that is, before the next elections. He needs to receive the money today, to be able to begin the construction. The amount needed for the building is of 1 billion dollars. Assume Bills receives the amount needed for the construction on January 1st, 2018. Bill is considering paying back the investors with different payback structures, all of them carrying an annual interest rate (or yield) of 2%
A. Calculate the price on January 1st, 2018, and on January 1st, 2021, for a zero-coupon bond (i.e. a bond with no coupon payments) with payback date of face value on January 1st, 2022. Calculate also the total payment, interest payment, and remaining face value on the 1st of January of every year between 2018, when the bond was issued, and 2022 for this bond