Reference no: EM132309556

1. Required Annuity Payments

Assume that your father is now 50 years old, plans to retire in 10 years, and expects to live for 25 years after he retires - that is, until age 85. He wants his first retirement payment to have the same purchasing power at the time he retires as $45,000 has today. He wants all of his subsequent retirement payments to be equal to his first retirement payment. (Do not let the retirement payments grow with inflation: Your father realizes that if inflation occurs the real value of his retirement income will decline year by year after he retires). His retirement income will begin the day he retires, 10 years from today, and he will then receive 24 additional annual payments. Inflation is expected to be 6% per year from today forward. He currently has $100,000 saved and expects to earn a return on his savings of 5% per year with annual compounding. To the nearest dollar, how much must he save during each of the next 10 years (with equal deposits being made at the end of each year, beginning a year from today) to meet his retirement goal? (Note: Neither the amount he saves nor the amount he withdraws upon retirement is a growing annuity.) Do not round intermediate steps.

2. Future Value of an Annuity

Find the future value of the following annuities. The first payment in these annuities is made at the end of Year 1, so they are ordinary annuities. Round your answers to the nearest cent. (Notes: If you are using a financial calculator, you can enter the known values and then press the appropriate key to fi nd the unknown variable. Then, without clearing the TVM register, you can "override' the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in many situations, to see how changes in input variables affect the output variable. Also, note that you can leave values in the TVM register, switch to Begin Mode, press FV, and find the FV of the  annuity due.)

a. $800 per year for 10 years at 8%.

b. $400 per year for 5 years at 4%.

c. $800 per year for 5 years at 0%.

Now rework parts a, b, and c assuming that payments are made at the beginning of each year; that is, they are annuities due.

d. $800 per year for 10 years at 8%.

e. $400 per year for 5 years at 4%.

3. Required Lump-Sum Payment

To complete your last year in business school and then go through law school, you will need $15,000 per year for 4 years, starting next year (that is, you will need to withdraw the first $15,000 one year from today). Your uncle offers to put you through school, and he will deposit in a bank paying 4.27%
interest a sum of money that is sufficient to provide the 4 payments of $15,000 each. His deposit will be made today.

a. How large must the deposit be? Round your answer to the nearest cent.

b. How much will be in the account immediately after you make the first withdrawal? Round your answer to the nearest cent.

c. How much will be in the account immediately after you make the last withdrawal? Round your answer to the nearest cent. Enter "0" if required.

4. Amortization Schedule

Consider a $35,000 loan to be repaid in equal installments at the end of each of the next 5 years. The interest rate is 11%.

a. Set up an amortization schedule for the loan. Round your answers to the nearest cent. Enter "0" if required

Year Payment Repayment Interest       Repayment of Principal       Balance

1 $ $ $ $

2 $ $ $ $

3 $ $ $ $

4 $ $ $ $

5 $ $ $ $

Total $ $ $

b. How large must each annual payment be if the loan is for $70,000? Assume that the interest rate remains at 11% and that the loan is still paid off over 5 years. Round your answer to the nearest cent.

c. How large must each payment be if the loan is for $70,000, the interest rate is 11%, and the loan is paid off in equal installments at the end of each of  the next 10 years? This loan is for the same amount as the loan in part b, but the payments are spread out over twice as many periods. Round your  answer to the nearest cent.

-Why are these payments not half as large as the payments on the loan in part b?

I. Because the payments are spread out over a longer time period, more principal must be paid on the loan, which raises the amount of each payment.

II. Because the payments are spread out over a longer time period, less interest is paid on the loan, which raises the amount of each payment.

III. Because the payments are spread out over a longer time period, less interest is paid on the loan, which lowers the amount of each payment.

IV. Because the payments are spread out over a shorter time period, more interest is paid on the loan, which lowers the amount of each payment.

V. Because the payments are spread out over a longer time period, more interest must be paid on the loan, which raises the amount of each payment.

5. Uneven Cash Flow Stream

a. Find the present values of the following cash flow strelms. The appropriate interest rate is 6%. Round your answers to the nearest cent. (Hint: It is  fairly easy to work this problem dealing with the individual cash flows. However, if you have a financial calculator, read the section of the manual that describes how to enter cash flows such as the ones in this problem. This will take a little time, but the investment will pay huge dividends throughout the course. Note that, when working with the calculators cash flow register, you must enter CF0 = 0. Note also that it is quite easy to work the problem with Excel, using procedures described in the Chapter 4 Tool lGt.)

Year Cash Stream A Cash Stream B

1 $100 $300

2 400 400

3 400 400

4 400 400

5 300 100

Stream A $

Stream B $

b. What is the value of each cash flow stream at a 0% interest rate? Round your answers to the nearest cent.

Stream A $

Stream B $