Your friend decides to purchase a home and takes a $15-$year, $$100,000$ mortgage with a mortgage rate of $4\mathrm{.}8\%.$ Her monthly mortgage payment would be $$780\mathrm{.}4.$ Please fill in the blanks. $(10)$

$\backslash$table$[[$Month$,\backslash$table$[[$Beginning$],[$balance of$],[$loan$]],\backslash$table$[[$Monthly$],[$payment$]],\backslash$table$[[$Monthly$],[$interest rate$]],\backslash$table$[[$Amount$],[$applied to$],[$interest$]],\backslash$table$[[$Amount$],[$applied to$],[$principal$]],\backslash$table$[[$Ending$],[$balance of$],[$loan$]]],[1,$$$100,000,$$$780\mathrm{.}4,$a$.,$b$.,$c$.,$d$.],[2,$e$.,$f$.,$g$.,$h$.,$i$.,j.]]$

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