SUBJECT: ANNUITY

1. Assume that a particular college basketball player is certain to go pro. He is 19 now and will likely earn $5 million per year for 10 years once he turns pro at the age of 22. If his first paycheck of $5 million dollars is due 3 years from today, what is the value today of his future earnings as a professional basketball player? Assume a discount rate of 15% per year. (3 pts)

a. If the discount rate is lower would the value today be lower or higher? WHY?

Click to find the Answer1[a]

b. If he expects to turn pro earlier, but still plans to play only 10 years, will the value of his earnings today be lower or higher? WHY?

Click to find the Answer1[b]

2. You want to have an income of $100,000 per year for 20 years when you retire. If you are 25 now, how much do you have to invest per year to reach your retirement goal? Assume that you will make your first deposit one year from now when you turn 26 and you will continue until you turn 65. You will withdraw your first $100,000 cash flow when you turn 66. Assume an interest rate of 12% per year throughout this problem. (2pts)

3. Austin Danger Powers was cryogenically frozen for 30 years. Assume that he had savings totaling $50,000 when he was frozen. If his money was invested at 10% for the 30 years he was frozen (from 1967 to 1997), how much of an annual cash flow (an annuity) could he fund starting in 1998 and lasting for 25 years? Assume a return of 10% per year throughout this problem. (2 pts)

4. You’ve found a $200,000 home that you want to buy. A mortgage broker gets you a 7% APR on a 30 year loan with monthly payments. Your first payment is due in one month.

(1) What will your monthly payments be? (5)

Click to find the Answer4[1]

(2) One option that the broker offers you is a point-paydown. You can pay an EXTRA "point" equal to $2000 (1% of the mortgage value) in return for a lower rate on the loan, 6.75% APR. What is the monthly payment in this case? That is, the loan is still $200,000. You just pay $2000 to your broker to get the lower rate, 6.75% APR.

Click to find the Answer4[2]

(3) If you are only planning to be in the house for 6 years, is this option a good deal? Use your answer (1) and (2) to answer this question. Use 7 % APR to evaluate.. (6)

Click to find the Answer4[3]

(4) 6 years into the mortgage, you sell the house for $225,000. After you pay off your mortgage balance (assume your mortgage rate is the very first one: 7% APR, no point down), how much of the proceeds from the sale will you be left with? (7)

Click to find the Answer4[4]

5. Kevin Brown, a pitcher for the Dodgers, recently became baseball's first "$100 million man". (As you know, Steve Austin was the $6 million man.) His contract calls for a $15 million payment upon signing (now), $10 million in the first year, and $15 million per year for 6 years after that, adding up to $115 million. Assume that all of his salary payments except for the signing bonus are paid at the ends of the years. What is the actual value of his contract if the appropriate discount rate is 10%? (6)

6. You are interested in a $20,000 car. One option for paying for it is a 48 month loan with an 8% APR and monthly payments starting one month after the purchase of the car.

a.What would your payments be? (5)

Click to find the Answer6(a)

b.The dealer offers you a special deal: Either $2000 cashback ($2000 off of the price of the car), or a reduced interest rate of 7.5% on the car loan. Which should you take?(6)

Click to find the Answer6(b)

c.You are also considering leasing the car for 48 months instead of buying it. The car will be worth $10,000 at the end of the lease, and the lease is figured based on an 8% APR and a $20,000 purchase price. If the first payment is due one month after you take the car, what will your lease payments be? (6)

Click to find the Answer6(c)

7. "Invest early and often." You often hear that, but why does it make sense? Consider two outcomes of your life: (1) you invest $5000 per year in the stock market, starting when you’re 25, or (2) you invest $10,000 per year in the stock market starting when you’re 35. The average annual return on the stock market is 12%. How much more or less will you have when you're 65 with the second path vs. the first path? (8)

8.You're negotiating for a new car. You are going to pay for the car with a 5-year loan at 7% per year, compounded monthly. Your loan payments will also be monthly. You've got the price down to $20,000, but you're still negotiating. For every $100 that you get the dealer to lower the price of the car, how much does your monthly payment decrease? Assume your first payment is due one month from today.

9. Let's say you resolve to drink one less beer per month for the next 40 years. Assume that this represents a savings of $3 per month. If you take that extra $3 and invest it each month in your retirement account, how much extra will you have when you retire in 40 years? Assume your retirement account earns 12% per year, compounded monthly.

10. Let’s say that during your salary negotiations with Lucasfilm you are given the following offer: either get $10,000 a year extra in salary for the next 40 years, or get $80,000 a year extra in pension for 25 years, starting 41 years from now. Assuming an interest rate of 12%, which should you take (ignore any tax considerations)? (10)

11. Luke Skywalker is negotiating to buy a new Landspeeder. The dealer, Jabba, is offering it for $25,000. Luke can get a 4-year loan with monthly payments at a 9% APR, compounded monthly.

1. What would Luke’s loan payments be if the first payment is due one month from today? (6)
   
   Click to find the Answer11[a]
   
   
2. Luke’s other option is to lease the Landspeeder. The Landspeeder has a residual value of $12,000 (meaning that at the end of the lease it is worth $12,000). This means that at the end of the lease you must either buy the Landspeeder for $12,000 or return it to the dealer. Assume a 4-year lease with monthly payments, the first payment is due next month and the rate is the same as for the loan. What would Luke’s lease payments be? (8)
   
   Click to find the Answer11[b]
   
   
3. Assume Luke took the lease and each month invested the difference between his lease payment and what he would have paid on the loan. If he can earn 9% compounded monthly on these monthly investments, how much will he have in his investment account at the end of the lease? Will he be able to buy the Landspeeder at its residual value? (6)

Click to find the Answer11[c]

12. You are working for Lucasfilm and your retirement plan is as follows: $10,000 per year will be invested for the next 40 years at a rate of return of 12% per year (the first investment is one year from now). When you retire, you will take your retirement plan savings and start withdrawing an annuity each year for 25 years. Your first withdrawal will occur 41 years from now. Assume that, while in retirement, your money will earn only 10% per year. How much of a yearly withdrawal will you be able to make? (10)

13. Let’s say you graduate from the Jedi Academy with $14,400 in student loans. Assume that these loans were disbursed as $300 every month over the previous 4 years. (That is, you received $300 every month for the past 4 years.) The stated rate of interest on these loans is 6%, compounded monthly. However, as is typical with student loans, the loans did not accrue interest during your schooling. Even though you were loaned the first $300 4 years ago, you have not been charged interest on it over the past 4 years. Thus the total amount you owe is only 48 times $300 instead of that amount plus interest.

1. How much did this interest deferral save you? That is, if your regular loans of $300 every month had been earning interest at the stated rate, what total amount would you owe now? (8)
   
   Click to find the Answer13(a)
   
   
2. If you owe $14,400 now and you intend to pay it back in monthly installments over the next 6 years, plus one lump sum of $5000 along with the 72^nd payment, how much will you have to pay per month (assume an interest rate of 6%, compounded monthly)? (8)

Click to find the Answer13(b)

14. You graduate and land that big job. It's Porsche Boxster time! You are negotiating with the dealer and you are trying to decide whether to buy or lease. He presents you with a 4 year lease: interest rate is 7% compounded monthly, purchase price is $40,000, buyout price is $25,000. What this means is that you are essentially borrowing $40,000, which you will repay in 48 equal monthly installments plus one lump payment at the end equal to $25,000 (or you just return the car, which they figure will be worth $25,000). He claims that based on these figures, your lease payment will be $530.

1. Is he telling the truth or is he overcharging you? EXPLAIN. (8 pts.)
   
   Click to find the Answer14[a]
   
   
2. Assuming that the purchase price and the buyout are correct, is he actually charging you a higher or lower interest rate? How can you tell? (5 pts.)

30a. Let's talk about the importance of investing early. You graduate and get a good job. By the time you're 25, you're in a position to start saving $200 per month for retirement. You plan to retire in 40 years, at the age of 65. You expect to earn 12% per year, compounded monthly, on your investments and you plan to put your first $200 away immediately. How much will you have when you retire? [8 pts]

30b. Let's say you procrastinate and wait until you're 35 to start saving. You still plan to retire at the age of 65, but now you've only got 30 years to save. How much more will you have to save per month in order to retire with the same amount of money as in part a? Assume that you will make your first payment in a month and make a total of 360 payments. [8 pts]

31. When Bill Clinton leaves office, he will get a $150,000 per year pension for life. His salary while in office was approximately $200,000 per year. For this question, assume annual payments and an interest rate of 8%, compounded annually. Assume he stays in office for 8 years and he expects to live for 30 years after leaving office. What was the total value of his compensation at the beginning of his presidency, one year before his first paycheck. (8 pts.)

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