$1.$ Assume the total cost of a college education will be $$354,000$ when your child enters college in $18$ years. You presently have $$93,000$ to invest. What annual rate of interest must you earn on your investment to cover the cost of your childs college education?$$

$2.$ At $5\mathrm{.}1$ percent interest, how long does it take to double your money? To quadruple it$?$

$3.$ According to the Census Bureau, in October $2016,$ the average house price in the United States was $$354,900.$ In October $2000,$ the average price was $$215,100.$ What was the annual increase in the price of the average house sold?$4.$ Youre trying to save to buy a new $$295,000$ Ferrari. You have $$80,000$ today that can be invested at your bank. The bank pays $3\mathrm{.}4$ percent annual interest on its accounts. How long will it be before you have enough to buy the car?$$

$5.$ Imprudential, Inc., has an unfunded pension liability of $$415$ million that must be paid in $20$ years. To assess the value of the firms stock, financial analysts want to discount this liability back to the present. If the relevant discount rate is $5\mathrm{.}2$ percent. What is the present value of this liability?

$6.$ You have just received notification that you have won the $$3$ million first prize in the Centennial Lottery. However, the prize will be awarded on your $100$th birthday $($assuming youre around to collect$),80$ years from now. What is the present value of your windfall if the appropriate discount rate is $8\mathrm{.}4$ percent?$7.$ Your coin collection contains fifty $1952$ silver dollars. If your grandparents purchased them for their face value when they were new, how much will your collection be worth when you retire in $2067,$ assuming they appreciate at an annual rate of $4\mathrm{.}3$ percent?$$

$8.$ In $1895,$ the first U$.$S$.$ Open Golf Championship was held. The winners prize money was $$150.$ In $2016,$ the winners check was $$1,800,000.$ What was the percentage increase per year in the winners check over this period? If the winners prize increases at the same rate, what will it be in $2040?$

$9.$ Although appealing to more refined tastes, art as a collectible has not always performed so profitably. During $2003,$ Sothebys sold the Edgar Degas bronze sculpture Petite Danseuse de Quatorze Ans at auction for a price of $$10,311,500.$ Unfortunately for the previous owner, he had purchased it in $1999$ at a price of $$12,377,500.$ What was his annual rate of return on this sculpture?$$

$10.$ The Brasher doubloon, which was featured in the plot of the Raymond Chandler novel, The High Window, was sold at auction in $2014$ for $$4,582,500.$ The coin had a face value of $$15$ when it was first issued in $1787$ and had been previously sold for $$430,000$ in $1979.$ At what annual rate did the coin appreciate from its minting to the $1979$ sale? What annual rate did the $1979$ buyer earn on his purchase? At what annual rate did the coin appreciate from its minting to the $2014$ sale?