In $11$ years you are planning on retiring and buying a house in$$ Oviedo, Florida. The house you are looking at currently costs $$$$90$ comma $000$ and is expected to appreciate $4$ percent each year. Assuming you can earn $9$ percent annually on your$$ investments, how much must you invest at the end of each of the next $11$ years to be able to buy this house when you$$ retire?

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Part $1$

a$.$ If the house you are looking at currently costs $$$$90$ comma $000$ and is expected to appreciate $4$ percent each$$ year, what will the value of the house be when you retire in $11$years$?$

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$($Round to the nearest$$ cent.$)$

b$.$ Assuming you can earn $9$ percent annually on your$$ investments, how much must you invest at the end of each of the next $11$ years to be able to buy this house when you$$ retire?

$$$

$($Round to the nearest$$ cent.$)$