Suppose the government decides to issue a new savings bond that is guaranteed to double in value if you hold it for $18$ years. Assume you purchase a bond that costs $$50.$

a$.$ What is the exact rate of return you would earn if you held the bond for $18$ years until it doubled in value? $($Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$.$If you purchased the bond for $$50$ in $2020$ at the then current interest rate of $\mathrm{.}28$ percent year, how much would the bond be worth in $2030?($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

c$.$In $2030,$ instead of cashing in the bond for its then current value, you decide to hold the bond until it doubles in face value in $2038.$ What annual rate of return will you earn over the last $8$ years? $($Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

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