e$.$ Assume that the average price of a new home is $$114,500.$ If the cost of a new home is increasing at a rate of $7\%$ per year, how much will a new home cost in eight years?

Note: Round your answer to $2$ decimal places.

f$.$ An investment will pay you $$7,000$ in $9$ years, and it also will pay you $$240$ at the end of each of the next $9$ years $($years $1$ through $9).$ If the annual interest rate is $5\%,$ how much would you be willing to pay today for this type of investment?

Note: Round your intermediate calculations and final answer to the nearest whole dollar.

g$.$ A college student is reported in the newspaper as having won $$7,500,000$ in the Kansas State Lottery. However, as is often the custom with lotteries, she does not actually receive the entire $$7\mathrm{.}5$ million now. Instead she will receive $$375,000$ at the end of the year for each of the next $20$ years. If the annual interest rate is $7\%,$ what is the present value $($today$$s amount$)$ that she won? $($ignore taxes$).$

Note: Round your answer to nearest whole dollar.