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 $$2,000$ in March $2040,$ but investors would receive nothing until then. Investors paid DMF $$610$ for each of these securities; so they gave up $$610$ in March $2020,$ for the promise of a $$2,000$ payment $20$ years later.

a$.$ Assuming you purchased the bond for $$610,$ what rate of return would you earn if you held the bond for $20$ years until it matured with a value $$2,000?$

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 $2030.$ 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 $2030,$ instead of cashing in the bond for its then current value, you decide to hold the bond until it matures in $2040.$ What annual rate of return will you earn over the last $10$ 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,,$\%$