The homework has $7$ problems. Please show your work. Do not just write down the final answers. I suggest that you use formulas to solve the problems. If you want to use a financial calculator, you may want to use it to double check the answer.

Unless otherwise stated, assume that the deposits or payments occur at the end of period and the first deposit or payment occurs at the end of the first period. Ignore taxes and transaction costs.

An investment offers $$150,000$ per year, every year for $20$ years. If the required annual return is $9$ percent, what is the value of the investment today? What would the value be if the payments occurred for forever?

If you save $$20,000$ per year, each year for the next $40$ years, how much money will you have in $40$ years? Assume that the annual rate of return is $9$ percent.

If you invest $$25,000$ a year at the beginning of each year for the next $30$ years in an account that earns $8$ percent annual return, how much will you have in the account in $30$ years?

John Watts has just retired after $35$ years with a company. His total pension funds have an accumulated value of $$2,000,000,$ and his life expectancy is $25$ more years. His pension fund manager assumes he can earn a $7$ percent annual return on his assets. What will be his yearly annuity $($i$.$e$.,$ the annual withdrawal amount$)$ for the next $25$ years?

An insurance agent is trying to sell you an immediate retirement annuity, which for a lumpsum fee paid today will provide you with $$100,000$ every year for the next $25$ years. You currently earn $8$ percent annual return on investments with comparable risk to the retirement annuity. What is the most you would pay for this annuity?

Your financial objective is to have $$5,000,000$ upon your retirement $40$ years from now. If you have committed to make an equal annual deposit into an investment account that provides $9$ percent annual return, how much will the annual deposit be$?$

If you invest $$30,000$ a year, every year in an account that earns $8$ percent annual return, how long will it take for the balance in the account to reach $$3,000,000?$