Perpetual Life Corp. has issued consol bonds with coupon payments of $$41.($Consols pay interest forever and never mature. They are perpetuities.$)$

a$.$

If the required rate of return on these bonds at the time they were issued was $15\mathrm{.}8\%,$ at what price were they sold to the public?

Price sold to the public $

b$.$

If the required return today is $5\%,$ at what price do the consols sell?

Current price $