A borrower takes out a $$200,000$ mortgage at a $5\%$ anmal interest rate with a $30-$year terna. They want beir annual payments to grow at a constant rate of $2\%$ per yoar. What is the initial pugment required to fally pay the loan?

A$)$ $$17,074$

B$)$ $$15,174$

C$)$ $$13,686$

D$)$ $$10,328$

$\backslash$table$[[,12/51/25,12/21/24],[$Crah$,51\mathrm{.}000,57309],[$Acrourtinucrivate$,62\mathrm{.}000,50\mathrm{.}500],[$Sontere debt inestmets livaldie for$-$sid$),3\mathrm{.}900,17800],[$Inevtary$,4$ase,$51\mathrm{.}300],[$Arepaidrent$,5,100,1900],[$Eowipnent$,254\mathrm{.}900,127200],[$Actumithed depreciation$-$squipment,D$4900.,[25200],[$Coprictes$,4200,47500],[$Total asess,$5114\mathrm{.}600,52$ n $100],[$Acrevets payible,$$44300,$$$40\mathrm{.}300],[$mosent lamesperille,$4\mathrm{.}000,6\mathrm{.}150],[$Slores und mapm porith,$1\mathrm{.}000,1,900],[$Shentere buss papibit,$8\mathrm{.}100,10000],[$Lencters leamparate,$*6000,$$$9200],[$Commen atsck $110$ pm$,100000,750000],[$Fiels ciplak temmon utock,$30000,30000],[$Brtainedeaming$,$$$7,400,31\mathrm{.}800],[,$$$914\mathrm{.}400,$$$202\mathrm{.}900]]$

Asestid idanation