221-hw1

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Feb 20, 2024

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INDENG221 | HW1 Q1. On September 1, 1998, Susan Chao bought a motorcycle for $10,000. She paid $l,000 down and financed the balance with a five-year loan at an APR of 9.6%, compounded monthly. She started the monthly payment exactly one month after the purchase, i.e., October 1998. In the middle of October 2000, she got a new job and decided to pay off the loan. If the bank charges her 1% prepayment penalty based on the loan balance, how much should she pay the bank on November 1, 2000? Answer:
INDENG221 | HW1 Q2. A well-known insurance company offers a policy known as the “Estate Creator Six Pay”. Typically the policy is bought by a parent or grandparent for a child at the child’s birth.The details of the policy are as follows: The purchaser (say, the parent) makes a payment of $750 at the child’s first, second and third birthday, and makes a payment of $800 at the child’s fourth, fifth and sixth birthday to the insurance company (there are six payments in total). No more payments are made after the child’s sixth birthday. When the child reaches age 65, he or she receives $250,000. If the effective annual rate (EAR) is 6% for the first six years and 7% for all subsequent years, is the policy worth buying? -> Since the NPV of the policy is negative, -$545.88, it is not worth buying.
INDENG221 | HW1
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INDENG221 | HW1 Q3. Your company is considering leasing a $120,000 piece of equipment for the next 10 years. Your company can buy the equipment outright or lease it. The annual lease payments of $15,000 are due at the beginning of each year. The lease includes an option for your company to buy the equipment for $25,000 at the end of the leasing period (i.e., 10 years). Should your company accept the lease offer if the EAR is 8%?
INDENG221 | HW1
INDENG221 | HW1 Q4. You are saving for your retirement. You have decided that one year from today you will deposit 2% of your annual salary in an account which will earn 8% per year. Your salary last year was $50,000, and it will increase at 4% per year throughout your career. How much money will you have for your retirement, which will begin in 40 years?
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INDENG221 | HW1 Q5. You must decide whether or not to purchase a new capital equipment. The cost the machine is $5,000. It will produce the following cash flow stream (0, $700, $900, $1000, $1000, $1000, $1000, $1250 $1375). Should you purchase the equipment if the EAR is 10%?
INDENG221 | HW1 Q6. When Marilyn Monroe died, ex-husband Joe DiMaggio vowed to place fresh flowers on her grave every Sunday as long as he lived. A bunch of fresh flowers that the former baseball player thought appropriate for the star cost about $5 when she died in 1962. Based on actuarial tables, “Joltin’ Joe” could expect to live for 30 years after the actress died. Assume that the APR, compounded weekly, is 10.4%. Also, assume that the rate of inflation, is 3.9% per year, when expressed as an APR, compounded weekly. Assuming that each year has exactly 52 weeks, what is the present value of this commitment?
INDENG221 | HW1 Q7. Your younger brother has come to you for advice. He is about to enter college and has two options open to him. His first option is to study engineering. If he does this, his undergraduate degree would cost him $12,000 a year for four years. Having obtained this, he would need to gain two years of practical experience: in the first year he would earn $20,000, in the second year he would earn $25,000. He would then need to obtain his master?s degree, which will cost $15,000 a year for two years. After that he will be fully qualified and can earn $40,000 per year for 25 years. His other alternative is to study accounting. If he does this, he would pay $13,000 a year for four years and then he would earn $31,000 per year for 30 years. The effort involved in the two careers is the same, so he is only interested in the earnings the jobs provide. All earnings and costs are paid at the end of the year. What advice would you give him if the market interest rate is 5%? A day later he comes back and says he took your advice, but in fact, the market interest rate was 6%. Has your brother made the right choice?
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INDENG221 | HW1 Q8. In January 1984, Richard “Goose” Gossage signed a contract to play for the San Diego Padres that guaranteed him a minimum of $9,955,000. The guaranteed payments were $875,000 for 1984, $650,000 for 1985, $800,000 in 1986, $1 million in 1987, $1 million in 1988, and $300,000 in 1989. In addition, the contract called for $5,330,000 in deferred money payable at the rate of $240,000 per year from 1990 through 2006 and then $125,000 a year from 2007 through 2016. If the EAR is 9% and all payments are made on July 1 of each year, what would the present value of these guaranteed payments be on January 1, 1984? If he were to receive an equal annual salary at the end of each of the five years from 1984 through 1988, what would his equivalent annual salary be? Ignore taxes throughout this problem.
INDENG221 | HW1 Q9. Ms. Adams has received a job offer from a large investment bank as an assistant to the vice president. Her base salary will be $35,000. She will receive her first annual salary payment one year from the day she begins to work. In addition, she will get an immediate $10,000 bonus for joining the company. Her salary will grow at 4% each year. Each year she will receive a bonus equal to 10% of her salary. Ms. Adams is expected to work for 25 years. What is the present value of the offer if the EAR is 12%?
INDENG221 | HW1 Q10. Justin Leonard has just arranged to purchase a $400,000 vacation home in the Bahamas with a 20% down payment. The mortgage has an 8% APR with monthly compounding and calls for equal monthly payments over the next 30 years. His first payment will be due one month from now. However, the mortgage has an 8-year balloon payment, meaning that the loan must be paid off then. There were no other transaction costs or finance charges. How big will Justin’s balloon payment be in 8 years?
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