It is January $2023$ and you are considering a real estate investment. A large building will generate $$50,000$ in annual rental income. If you purchase the real estate, and own it in perpetuity, you are expected to raise rent over time by a $2\mathrm{.}5\%$ constant growth rate in order to keep pace with inflation.

If the expected rate of return in the real estate market is $8\%,$ what is the present value of this investment? Would you buy this building if it is for sale for $$850,000?$ Please type your solution to both questions below and show your work.