In ten years, you are planning to retire and buy a house in Tweed Heads, New South Wales. The house you are looking at currently costs $$100,000$ and is expected to increase in value each year at a rate of $5\%.$ Assuming that you can earn $10\%$ annually on your investments, how much must you invest at the end of each of the next ten years to be able to buy your dream home when you retire? Question $6[0\mathrm{.}5$ mark$]($Perpetuities$)$ What is the present value of the following? $($a$)$ A $$100$ perpetuity discounted back to the present at $9\%($b$)$ A $$95$ perpetuity discounted back to the present at $5\%$