Please show your work for each problem.

6. Your objective is to have $10,000,000 in an account that earns 8% annual return when you retire in 40 years. a) If you make an equal deposit at the end of every year to the account for the next 40 years, what is the annual deposit? Assume that your first deposit occurs at the end of next year. b) You retire after 40 years and have $10,000,000 in the account as planned. You expect to live for another 25 years after retirement. Assume that you leave the $10,000,000 in the account that continues to earn 8% annual return. You plan to make an equal withdrawal from the account every year for the next 25 years. The first withdrawal is made at the end of the first year after your retirement and the account balance would be depleted after you make the 25^th How much can you withdraw at the end of each year for the next 25 years?

7. You have found your dream home. The selling price is $400,000. You will put $80,000 as down payment and obtain a 30-year fixed-rate mortgage loan at 6 percent annual interest rate for the rest. a) You are required to make an equal payment every month for 360 months to pay off the balance on the loan. Assume that the first payment begins in one month after you obtained the loan. What will each monthly payment be? b) If you want to pay off the remaining principal on your mortgage loan after 10 years (i.e., 120 months), how much will you have to pay? Assume that you have never missed your payments during the first ten years after you obtained the loan. The bank that you obtained the loan from imposes no charges for early payoff of the loan.

Ignore transaction costs and taxes for the problems 8&9.

8. You are scheduled to receive annual payments of $150,000 for each of the next 20 years. The annual rate of return is 8 percent. What is the difference in the future value in year 20 if you receive these payments at the beginning of each year rather than at the end of each year?

9. You make the following deposits for the next five years into an investment account. All deposits are made at the end of the year and the first deposit occurs one year from now. No more deposits are made after year 5. You will leave all the money in the account until year 30. If you earn 8 percent annual return for the first five years and 6 percent annual return for all subsequent years, how much will you have in the account at the end of year 30?

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Year Deposit

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1 $100,000 2 $150,000 3 $200,000 4 $250,000 5 $300,000 _____________________________

10. A bond has 20 years remaining to maturity. The annual coupon rate of the bond is 8 percent. The bond makes annual coupon payments. The next coupon payment occurs one year from today. The par value (or face value) of the bond is $1,000. If the annual yield to maturity (or the required rate of return) on the bond is 6 percent, find the current bond price (or bond value).