A person deposits $$10,000$ ?on January $1,2007$ ?earning interest at the rates given in the table. Let P be the accumulated value under the investment year method, Q the accumulated value under the portfolio yield method, and R where the balance is withdrawn at the end of every year and is invested at the new money rate. Find the value of P$,$ ?Q$,$ ?and R on January $1,2012$

Calendar Year of Original Investment Portfolio Rates Investment Year Rate (in %) (in %) Y i i i ik y+5 2007 9.25 8.75 8.70 8.75 9.50 9.35 2008 8.75 9.10 9.75 8.90 9.00 8.95 2009 9.40 9.40 9.70 9.70 9.95 10.50 2010 9.20 9.65 9.85 9.70 9.80 10.10 2011 10.55 10.45 10.85 9.45 9.70 10.35