$1.$ You are trying to save to buy a Ferrari when you are $45$ years old. You have $$20,000$ today that can be invested in the bank. You think that a new Ferrari will cost $$340,000$ when you buy it$.$ Assume that you are twenty years old now. What annual rate of interest must you earn on yourinvestment to cover the cost of Ferrari? $2.$ You just received a notification that you have won the $$2$ million prize in the Lottery. However, the prize will be awarded on your $50$th birthday, $30$ years from now. What is the present value of your prize if the appropriate discount rate is $7\%?3.$ The monthly interest rate on credit cards increases to $4\mathrm{.}5\%.$ What will be the effective annual rate? What will be the annual percentage rate? $4.$ You want to be a millionaire when you are $60$ years old, $40$ years from today. a$.$ You plan to save the same amount every year, starting today, and deposit it in the bank until you are $59.$ So$,$ you will make your last deposit when you are $59.$ How much do you have to save each month if you can earn an APR of $12\%?$ b$.$ How much do you need to save each year if you wait $10$ years before you begin your deposits?