$(15$ pts$)$ I ask my friends Brittney and Leah if I can borrow $$500$ from them. I promise to fay them back after one year. Both friends are willing to loan me the money as long as I pay them the original $$500$ plus a little extra at the end of the year. Brittney wants $$505$ while Leah wants $$510.$

a $(5$ pts$)$ For Leah, $$510$ is the value of lending me $$500$ today.

b $(5$ pts$)$ Brittney's discount rate is: $($select one$)$

i$.$ higher than Leah's

ii$.$ lower than Leah's

iii. the same as Leah's

c $(5$ pts$)$ I decide to borrow the money from Brittney. However, I change the terms of our agreement. I ask Brittney if I can borrow $$500$ from her today and pay her back $$515$ three years from now. Assuming her discount rate stays the same, will Brittney still loan me the money? $($select one$)$