Assignment:
Part 1: Future value
Construct a table and a graph showing the relationship between interest rates, time, and future value by showing how $10,000 would grow each successive year over a 20 year period atdifferent interest rates. Use $10,000 for your present value and calculate the future value of this $10,000 each year over the 20 year period at 0%, 2%, 5%, 8%, 11%, 14%, 17%, and 20% compounded annually. Future Value should be the y-axis for your graph and years (or time) should be your x-axis and you should end up with a line for each interest rate on your graph. Please insert your graph (chart) under your table of future values.
Part 2: Present value
Construct a table and a graph showing the relationship between interest rates, time, and present value by showing how $10,000 pushed a year further into the future over a 20 yearperiod would be discounted at different interest rates. Use $10,000 for your future value and calculate the present value of this $10,000 each year over the 20 year period at 0%, 2%, 5%, 8%,11%, 14%, 17%, and 20% compounded annually. Present Value should be the y-axis for yourgraph and years (or time) should be your x-axis and you should end up with a line for each interest rate on your graph. Please insert your graph (chart) under your table of present values.
Part 3: Annuity
Prof. Washington has a self-managed retirement plan through his University and would like to retire in 10 years and wonders if his current and future planned savings will provide adequate future retirement income. Here's his information and goals.
Prof. Washington wants a 25-year retirement annuity that begins 10 years from todaywith an equal annual payment equal to $70,000 today inflated at 3% annually over 10 years.
His first retirement annuity payment would occur 10 years from today.He realizes hispurchasing power will decrease over time during retirement.
? Prof. Washington currently has $280,000 in his University retirement account. He expectsthese savings and any future deposits into his University and any other retirement account will earn 7.5% compounded annually. Also, he expects to earn this same 7.5% annual return after he retires.
Answer the following questions to help Prof. Washington finalize his retirement planning.
1. What is Prof. Business' desired annual retirement income in the first year, i.e., the retirement income he wants 10 years from today?
2. Assuming that inflation is zero from year 10, how much will Prof. Washington need 10years from today to fund his desired retirement annuity?
3. Assume that inflation is zero from year 10. In addition to the $280,000 balance today,Prof. Washington will fund his future retirement goal from question 2 by making 10 annual equal deposits at 7.5% compounded annually into his retirement accounts starting a year from today (the last deposit will be made when Prof. Washington retires). How large does this annual deposit need to be in addition to the initial $280,000 invested in Prof. Business' retirement fund?
4. Assume that inflation is 3% during the entire period, even after retirement. -I got rid of some unnecessary sentences here- Prof. Washington is worried about his purchasingpower eroding during retirement. He would like his first retirement withdrawal to be equal to the amount you found in #1, and then he increase each successive retirement withdrawal by 3% annually over the remaining 24 withdrawals. How much will Prof. Washington need now at retirement given Prof. Washington's 7.5% expected return?
5. In addition to the $280,000 balance today, Prof. Washington will fund his adjusted future retirement goal from question 4 by making 10 annual equal deposits at 7.5% compounded annually into his retirement accounts starting a year from today (the last deposit will be made when Prof. Washington retires). How large does this annual deposit need to be in addition to the initial $280,000 invested in Prof. Washington's retirement fund?
Part 4. NPV
Robert, the sophomore 20-year-old star quarterback of the university soccer team, is approached about skipping his last two years of college and entering the professional soccer draft. Robert expects that his soccer career will be over by the time he is 32 years old. Talent
scouts estimate that Robert could receive a signing bonus of $15 million today, along with a four-year contract for $2 million per year (payable at the end of each year). They further estimate that he could negotiate a contract for $4 million per year for the remaining eight years of his career. The scouts believe, however, that Robert will be a much higher draft pick if he improves by playing two more years of college soccer. If he stays at the university, he is expected to receive a $25 million signing bonus in two years, along with a five-year contract for $3 million per year. After that, the scouts expect Robert to obtain a five-year contract for $5 million per year to take him into retirement. Assume that Robert can earn a 8% return over this time.
1. What is the present value today (when Robert is 20) of the QB's future expected NFL earnings if he enters the NFL now?
2. What is the present value today (when Robert is 20) of the QB's future expected NFL earnings if he finishes his last 2 years of college enters the NFL 2 years from now?
3. Should Robert stay in college or go to the NFL now?
Part 5. Monthly compounding
Bobby Brown decides to buy a Nissan Maxima. After paying a down payment and taxes, Bobby Brown can finance the rest of the purchase price with a loan of $27,000 for 60 months at a special finance rate offered by Nissan: 0.9% APR compounded monthly.
Answer the following.
1. What is the effective annual rate charged on this car loan?
2. What would be Bobby Brown's monthly payment under this loan?
3. Bobby Brown also discovers instead of the special finance rate he could receive $1500 cash back that he can use as an additional down payment which would lower his loan amount by the cash back amount. At what APR would Bobby Brown have the same monthly payment with the cash back option as he would with the special finance rate offer that you found in the last question?
4. Bobby Brown finds he can get 2.0% APR Financing if he elects the cash back option. What will his monthly payment be under this option and should he elect this cash back option over Nissan's special APR financing option?