A local bank advertises the following deal: "Pay us $$100$ at the end of each year for $12$ years and then we will pay you $($or your beneficiaries$)$ $$100$ at the end of each year forever."

$1.$ Calculate the present value of your payments to the bank if the interest rate is $7\mathrm{.}25\%.$

$2.$ What is the present value of a $$100$ perpetuity deferred for $12$ years if the interest rate is $7\mathrm{.}25\%?$