Problem # $1$: A loan is amortized over $7$ years, with monthly payments at a nominal rate of $7\mathrm{.}1\%$ compounded monthly. The first payment is $$1000,$ paid one month from the date of the loan. Each succeeding monthly payment will be $3\%$ lower than the prior one. What is the outstanding balance immediately after the $30$th payment is made?

Problem #$1$:

Answer correct to $2$ decimals.