$(1)$ Grace wants to save $$1,000,000$ for retirement. She expects to earn a $7\%$ return on her investment. Starting at the end of this year, she will save the same amount each year for $37$ years. How much must she save each year to achieve her goal?

$(2)$ Henry wants to save $$200,000$ for a down payment on a house. At the end of each year, he plans to save $$10,000$ in an account paying $4\%$ interest. How long will it take for him to reach his savings goal?

$(3)$Ion Blue Engines is going to lease a factory for $$91,000$ per year for the next $7$ years. Lease payments are due at the beginning of each year. If the discount rate is $6\%,$ what is the present value of the lease payments?

$(4)$You have saved for retirement in an account that earns $5\%$ interest. The funds will last for exactly $25$ years with the first withdrawl of $$56,000$ occuring $1$ year from today. To account for inflation, you plan to increase your withdrawls by $1\%$ per year. How much have you saved in your account?

$(5)$You plan to retire in $40$ years. When you retire, you would like to have saved $$4,500,000.$ To achieve this goal you will deposit an equal amount at the end of each year in a savings account that will pay $7\%.$ What Excel formula can you use to find the amount you must save each year?

$(6)$You would like to find the future value of an ordinary annuity that will pay $$3,000$ per year for $10$ years. If the discount rate is $10\%,$ which formula could you use to find the future value of the annuity?