Euture value of an annuity$)$ In $7$ years you are planning on retiring and buying a house Oviedo, Florida. The house you are looking at currently costs $$80,000$ and is expected to $$crease in value each year at a rate of $4$ percent. Assuming you can earn $13$ percent annually on your investments, how much must you invest at the end of each of the next $7$ years to be able to buy your dream home when you retire?

a$.$ If the house you are looking at currently costs $$80,000$ and is expected to increase in value each year at a rate of $4$ percent, what will the value of the house be when you retire in $7$ years?

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

b$.$ Assuming you can earn $13$ percent annually on your investments, how much must you invest at the end of each of the next $7$ years to be able to buy your dream home when you retire?

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