In March $2020,$ Daniela Motor Financing $($DMF$),$ offered some securities for sale to the public. Under the terms of the deal,

DMF promised to repay the owner of one of these securities $$5,000$ in March $2050,$ but investors would receive nothing

until then. Investors paid DMF $$1,250$ for each of these securities; so they gave up $$1,250$ in March $2020,$ for the promise

of a $$5,000$ payment $30$ years later.

a$.$ Assuming you purchased the bond for $$1,250,$ what rate of return would you earn if you held the bond for $30$ years

until it matured with a value $$5,000?$

Note: Do not round intermediate calculations and enter your answer as a percent, rounded to $2$ decimal places,

e$.$g$.,32\mathrm{.}16.$

b$.$ Suppose under the terms of the bond you could redeem the bond in $2035.$ DMF agreed to pay an annual interest

rate of $1\mathrm{.}5$ percent until that date. How much would the bond be worth at that time?

Note: Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.$

c$.$ In $2035,$ instead of cashing in the bond for its then current value, you decide to hold the bond until it matures in

What annual rate of return will you earn over the last $15$ years?

Note: Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places,

e$.$g$.,32\mathrm{.}16.$