Mr$.$ Bill S$.$ Preston, Esq., purchased a new house for $$$$110,000.$ He paid $$20,000$ upfront and agreed to pay the rest over the next $20$ years in $20$ equal annual payments that include principal payments plus $13$ percent compound interest on the unpaid balance. What will these equal payments$$ be$?$

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Part $1$

a$.$Mr$.$ Bill S$.$ Preston, Esq., purchased a new house for $$$$110,000$ and paid $$$$20,000$ upfront. How much does he need to borrow to purchase the$$ house?