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 $$5,000$ in March $2050,$ but investors would receive nothing until then. Investors paid DMF $$1,450$ for each of these securities; so they gave up $$1,450$ in March $2020,$ for the promise of a $$5,000$ payment $30$ years later.

a$.$ Assuming you purchased the bond for $$1,450,$ what rate of return would you earn if you held the bond for $30$ years until it matured with a value $$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 $1\mathrm{.}3$ 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 $2050.$ 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$.,32\mathrm{.}16.$

$\backslash$table$[[$a$.$ Rate of return,$\%$