Solve the following time value problems:

$1.$ A company needs to have $$2,500,0006$ years from now for a building project. In an investment opportunity that pays $9\%,$ how much will have to be deposited today in order to reach their goal?

$2.$ A company has an opportunity to invest $$9,000$ at $4\%.$ How much will have accumulated in $15$ years?

$3.$ An individual plans to invest $$2,500$ at the end of each year at $8\%.$ How much will they have accumulated in $20$ years?

$4.$ A company plans to invest $$100,000$ at the beginning of each year at $5\%.$ How much will be accumulated at the end of $5$ years?

$5.$ How much money would have to be deposited today at $10\%$ in order to make a withdrawal of $$20,000$ at the end of the each year for the next $3$ years?

$6.$ A company has $$25,000$ to invest, and needs to accumulate at least $$40,000$ in $10$ years. How high must the interest rate be in order to achieve this goal?

$7.$ A company has $$15,000$ today, and needs to have $$30,000.$ If they have a $9\%$ investment opportunity, how many years ill it take to reach their goal?