Monopoli Manufacturing, Inc., is considering the purchase of a new packaging machine for $$880,000.$ For income tax purposes, Monopoli will depreciate the new machine by the straight$-$line method to a zero salvage value over eight years. However, the project is expected to end after seven years when the machine will have a market value of $$80,000.$

The new machine will allow Monopoli to reduce its $($before tax$)$ operating expenses the first year, and these savings will increase by $5\%$ per year through the seventh year. Monopoli's required rate of return on such projects is $15\mathrm{.}5\%,$ its average income tax rate is $22\%,$ and its marginal income tax rate is $28\%.$

Required: What minimal amount of first year's savings is necessary to justify acquiring the packaging machine?

$($Use the HP $10$bii financial calculator if needed and show me what you typed in$)$