Q$3$: The future worth for an initial single$-$payment investment of $$10,000$ after $10$ years is calculated as $$48,068.$ The expected annual inflation rate is $5\mathrm{.}5\%$ for ten years.

a$)$ Calculate the rate of return for this investment $(10$ points$)$

b$)$ Calculate the real $($inflation$-$free$)$ rate of return for this investment $(7$ points$)$

c$)$ Calculate the current purchasing power for the future value of the investment $($ $$48,06810$ years in the future$)(7$ points$)$