Peter purchased a machine for $$400,000.$ He paid $16\%$ of the value as a down payment and received a loan for the balance at $7\mathrm{.}05\%$ compounded annually. He had to make payments of $$4,443\mathrm{.}55$ at the end of every month to settle the loan.

a$.$ How many payments were made?

A full solution for the number of payments should be shown. Submit your solution.

payments

Round up to the next payment period