Suppose you bought a bond with an annual coupon rate of $4$ percent one year ago for $$800.$ The bond sells for $$850$ today.

a$.$ Assuming a $$1,000$ face value, what was your total dollar return on this investment over the past year?

b$.$ What was your total nominal rate of return on this investment over the past year? $($Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

c$.$ If the inflation rate last year was $2$ percent, what was your total real rate of return on this investment? $($Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

$\backslash$table$[[$a$.$ Total dollar return,,$],[$b$.$ Nominal rate of return,,vdots