You are considering investing in a financial instrument that pays $$30$ dollars at the start of each year for $10$ years. If you require a rate of return of $4\%$ per year for such an investment, what is the maximum price you would be willing to pay for this financial instrument?

You decide to invest $$4,000$ in an account that guarantees $3\%$ interest per year compounded annually. How much will you have after three years?

You would like to retire in $30$ years and you have calculated that you will need to save $$2$ million dollars by then to retire comfortably. How much must you put into your retirement savings account at the end of each year between now and retirement $($assume an interest rate of $3\mathrm{.}5\%$ annually$)?$

If you are able to save $$15,000$ per year starting immediately for the next $50$ years, how much will you have saved by the end of the $50$ years? How much will you have saved by the end of the $40$th year?

You really want to be able to buy a boat so you can take your friends out for cruises, but have only saved $$200.$ You are willing to borrow some money in addition to using your savings. You determine that you can afford to make loan payments of $$4,000$ per year beginning at the end of the year and want to have the loan paid off in seven years. What is the maximum value of the loan you can take and the total value of the boat you can afford? Assume an interest rate of $5\mathrm{.}5\%.$