The Following Problem Requires Some of the Following Present Value

The following problem requires some of the following present value information:
$\begin{array} { | l | l| } \hline \text { PV af an arthary annuity for } 20 \text { periods at } 12 \% & 7.46944 \\\hline \text { PV af an ardinary annuty for } 19 \text { periods at } 12 \% & 8.36497 .36578 \\\hline \text { PV af an arthary annuty for } 18 \text { periods at } 10 \% 12 \% & 8.20147 .24967 \\\hline \text { PV af } 1 \text { for } 20 \text { periods at } 10 \% 12 \% & 0.10367\\\hline\end{array}$
Bioco sold a patent on a new laser process to Agent Co.The sales agreement,which was signed on January 1,2011,requires Agent Co.to pay Bioco $2 million immediately.In addition,Agent is required to pay 500,000 each December 31 for 20 years starting with December 31,2011.Agent and Bioco estimate that 12 percent is an appropriate interest rate for this arrangement.
Required:
a.Compute the present value of the receivable on Bioco's books on January 1,2011 immediately after receiving the $1 million down payment.
b.Compute the present value of the receivable on Biotech's books on December 31,2011.
c.Compute the present value of the receivable on Biotech's books on December 31,2012.