$3\mathrm{.}1\mathrm{.}2$S A loan is amortized over five years with monthly payments at a

nominal interest rate of $9\%$ compounded monthly. The first pay$-$

ment is $1000$ and is to be paid one month from the date of the loan.

Each succeeding monthly payment will be $2\%$ lower than the prior

payment. Calculate the outstanding loan balance immediately af$-$

ter the ${40}^{th}$ payment is made.