On January 1, 2011, Gray Company sold $1,000,000 of 10% bonds, due January 1, 2021. Interest on these bonds is paid on July 1 and January 1 each year. According to the terms of the bond contract, Gray must establish a sinking fund for the retirement of the bond principal starting no later than January 1, 2019. Since Gray was in a tight cash position during the years 2011 through 2016, the first contribution into the fund was made on January 1, 2017.

Case 1:Assume that, starting with the January 1, 2017 contribution, Gray desires to make a total of four equal annual contributions into this fund. Compute the amount of each of these contributions assuming the interest rate is 8% compounded annually.

Case 2:Assume, instead, that starting with the January 1, 2019 contribution, Gray desires to make a total of five equal semiannual contributions into this fund. Compute the amount of each of these contributions assuming the annual interest rate is 12%, compounded semiannually.

This is the question I am currently working on, I have tried to check my solutions again those I've found here but I keep getting stuck on how to choose which factor to use. I figured both case 1 and 2 as annuities due, but every solution I've worked through has case 2 as an ordinary annuity. Can you tell me how they determined that?