A local bank advertises the following deal: Pay us $$100$ at the end of each year for $11$ years and then we will pay you $($or your beneficiaries$)$ $$100$ at the end of each year forever.

a$.$

Calculate the present value of your payments to the bank if the interest rate available on other deposits is $8\mathrm{.}50\%.$

b$.$

What is the present value of a $$100$ perpetuity deferred for $11$ years if the interest rate available on other deposits is $8\mathrm{.}50\%.$