Potter & Lopez Inc. just sold a bond with $50$ warrants attached. The bonds have a $20-$year maturity and an annual coupon of $12\%,$ and they were issued at their $$1,000$ par value. The current yield on similar straight bonds is $15\%.$ What is the implied value of each warrant?

a$.$ $$4\mathrm{.}14$

b$.$ $$3\mathrm{.}76$

c$.$ $$4\mathrm{.}56$

d$.$ $$4\mathrm{.}35$

e$.$ $$3\mathrm{.}94$