You will retire $4$ years from today. At retirement you need to pay $$100,$ and then after a year $$10,$ and finally two years after that $($or on the end of the seventh year from today$)$ a final $$5$ to buy an apartment in a continuing care facility. You have saved today $$50,$ and you plan to save $$40$ next year and then $$30$ each year until and including the year of your retirement. The interest rate is $5$ percent per year. Will you have enough money saved for your purchase?