$($Annuity payments$)$ Emily Morrison purchased a new house for $$200,000.$ She paid $$30,000$ upfront and agreed to pay the rest over the next $25$ years in $25$ equal annual payments that include principal

payments plus $14$ percent compound interest on the unpaid balance. What will these equal payments be$?$

a$.$ Emily Morrison purchased a new house for $$200,000$ and paid $$30,000$ upfront. How much does she need to borrow to purchase the house?

$($Round to the nearest dollar.$)$