Problem $37\mathrm{.}16$

A loan is amortized over five years with monthly payments at a nominal

interest rate of $9\%$ compounded monthly. The first payment is $1,000$ 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 after the $40$th payment is made.

answer should be $$6889\mathrm{.}11$