I am still confused about this problem. Can you go in deeper detail on how to solve this problem?

1. (Geometric average rate of return: Long-run performance) The table below shows the performance of Fidelity Magellan Fund (FMAGX) and SPDR S&P 500 ETF Trust (SPY) for each full calendar year over the Period d 2008-2013 2008 2009 2010 2011 2012 2013 ar -49.40% 36.83% 1 1 .55% 1.96% FMAGX 41.13% 26.30% 12.41% 14.88% 17.99% 15.84% 35.30% 321 3% SPY (a) Calculate the geom (b) If the initial investment at the beginning of 2008 was $10,000, what was the market value of the investment (S) in FMAGX at the end of 2013? Calculate (c) If the initial investment at the beginning of 2008 was S10,000, what was the market value of the investment (S) in SPY at the end of 2013? Calculate the whole-period return(% (d) Which investment yields better performance over the whole period 2008-2013? (e) In part (a), calculate the performance differential (%) between FMAGX and SPY using SPY as benchmark. (f) In parts (b) and (c), lculate the performance differential (%) between FMAGX and SPY using SPY comme of return (annual; %) for both FMAGX and SPY ear rn Solutions: (a) Geometric average return of FMAGX (1-0.4940) (1+0.4113+1241) 0.55) (1+0.1799) +0.3530) (6 1.1 33485-(1%)''6 r,-1.13348541/6)-l-)r.* 2.11%, Noted Using a calculator, 1/6s0166666667 then enter 1.1334850.166666667to get 1.133485 (1/6 1.021102.. ri-I . 1 3 348541 /6)-1 0.02 1 1-2. I 196 Geometric average return of SPY 1-0.3683)+0.2630) 1+0.1488)*1+0.0196) (1+0.1584) 1+0.3213) P6 1.430370-(1%)% re~ 6.15% (b) 10,000 * 1 . 1 33485-1 1 ,334.85; ( 1 1 ,334.85-10,000), 10,000-13.35% (c) 10,000* 1.430370 14.303.70; ( 14,303.70-10,000)/10,000-43,04 % (d) SPY (e) 2.11-6.154.04 FMAGX underperforms when using SPY as benchmark. (f) 13.35-43.04-29.69(%) over 6 years. Solving r, which is the geometric average rate of retu (W/Vo)=( 1 + re )"N,-w(1 + ri ) "N (The ending value) Long-run (or buy-and-hold) return = (Vi-Vo)/Vo omparison A-capital or amount due, V-the principal amount, r the fixed annual interest rate At the end of the first year: A-V(1+r)