Principles of Finance HW 3

________ is simply the interest earned in subsequent periods on the interest earned in prior periods. A) Compound interest B) Quoted interest C) Simple interest D) Anticipated interest

A) Compound interest

Your family plans to spend $25,000 on a car for you upon graduation from college. If you will graduate in three years and your family can earn 3.125% annually on their investment, how much money must they set aside today for your car? A) $22,795.45 B) $23,243.66 C) $21,387.36 D) $23,009.21

A) PV= FV / (1+r)^n = 25,000/ (1.3125)^3= $22,795.45

Your manufacturing firm has just secured a sale to the federal government with payment of $480,000 due in nine months. You have asked your bank for cash today with the stipulation that you will give the proceeds from the government contract to the bank in nine months. The bank has agreed to your request if you allow them to discount the cash flows at an annual rate of 6%. How much will the bank pay you today under this agreement? A) $459,475 B) $466,889 C) $480,000 D) $476,739

A) PV= FV / (1+r)^n = 480,000/(1.06)^0.75= $459,475

Upon taking his first job out of college, your Dad earned an annual salary of $33,000 and set a goal to earn $100,000 per year. If his salary increased at an average annual rate of 5.5%, how long did it take to reach his goal? A) 20.71 years B) 16.31 years C) 35.31 years D) 8.54 years

A) n=ln(FV/PV) / ln(1+r)= ln(100,000/33,000) / ln(1.055)= 20.71

Your production manager informs you that currently the firm is producing 1,348 heating units per month but has plans to increase production at a rate of 5% per month until the firm is producing 3,000 units per month. How many months will this take? A) 16.40 months B) 15.07 months C) 14 months D) There is not enough information to answer this question.

A) n=ln(FV/PV) / ln(1+r)= ln(3,000/1,348) / ln(1.05) =16.40

Your grandfather likes to tell the story about how he started his ranch with 100 head of cattle and grew the ranch to 2,500 head of cattle. He said "My plan was simple: grow the number of head of cattle at a rate of 10% per year." How long did it take him? A) 33.77 years B) 27.65 years C) 38.63 years D) 31.43 years

A) n=ln(FV/PV)/ln(1=r) = ln(2500/100) / ln(1+0.1) = 33.77

Buying your own home is often mentioned as "the best investment you can make." In 1964, the average home sale price was $19,600. By 2009, the average home sale price had risen to $272,900. What was the average annual rate of change in the price of houses over this 45 year time period? A) 6.03% per year B) 12.16% per year C) 3.74% per year D) 10.52% per year

A) r=(FV/PV)1/n-1= (272,900/19,600)1/45-1= 6.03%

You gave your little sister two rabbits for Easter three years ago and now she has 64 of the cute little bunnies. What is the average annual rate of increase in the number of rabbits your sister owns? Note: Your parents are not very pleased with you right now. A) 217.5% B) 400.0% C) 521.8.00% D) The TVM equations are designed for currency amounts and cannot be used for non-financial calculations such as this one.

A) r=(FV/PV)1/n-1= (64/2)1/3-1=2.17.5%

Your trust fund will pay you $100,000 in six years when you turn 25. A shady financial institution has encouraged you to sign away the rights to your trust fund in exchange for cash today. Would you prefer that the financial institution use a discount rate of 8% or 10% to determine the value of your lump sum payment? Why? A) Use 8% because the lump sum payment of $63,017 is greater than the 10% discounted value of $56,447. B) Use 10% because the lump sum payment of $63,017 is greater than the 10% discounted value of $56,447. C) Use 8% because the lump sum payment of $62,741 is greater than the 10% discounted value of $55,839. D) Use 10% because the lump sum payment of $62,741 is greater than the 10% discounted value of $55,839.

A) PV = FV/(1+r)^n = $100,000/(1.08)^6= $63,016.96, whereas = $100,00/(1.10)^6=$56,447.39

In two years Brandon plans to enroll at Umpqua University, a prestigious university in the Pacific Northwest of the USA. If the current tuition is $23,500 per year and is expected to increase at a rate of 6% per year, how much will Brandon pay in tuition his first year of school? (His first tuition payment is exactly two years from today.) In his fourth year? (His last tuition payment is exactly 5 years from today) (Rounded to the nearest dollar.) A) $23,500 and $31,448 B) $26,405 and $31,448 C) $23,500 and $29,668 D) $26,405 and $29,668

B) FV=PV(1+r)^n= $23,500*(1.06)^2= $26,405 and $23,500*(1.06)^5=$31,448

The question "What is the current value of an amount of cash that will be received at a specific time in the future?" is best answered by which form of the TVM equation? A) PV = (FV/PV)1/n - 1 B) PV = FV/(1+r)^n C) PV = PV × (1 + r)n

B) PV = FV/(1+r)^n

In four years your oldest child will be in 10th grade, at which point you and your family plan to vacation in Europe. You estimate that you will need $25,000 for the trip. How much do you need to set aside today if you can place your money in an investment vehicle earning an average of 4.25% per year? A) $21,435.77 B) $21,165.85 C) $20,215.55 D) $20,998.34

B) PV= FV / (1+r)^n = 25,000/ (1.0425)^4= 21,165.85

An investment promises a payoff of $995 two and one-half years from today. At a discount rate of 4.5% per year, what is the present value of this investment? A) $914.67 B) $891.32 C) $808.44 D) There is not enough information to answer this question.

B) PV= FV / (1+r)^n = 995 / (1.045)^2.5= 891.32

In 1930, the highest paid player in major league baseball was Babe Ruth of the New York Yankees, with an annual salary of $80,000. In 2017, the highest paid player in major league baseball was Clayton Kershaw of the Los Angeles Dodgers with a salary of $35,571,000. What was the average annual rate of growth in the top baseball salary over this time period? A) 10.41% B) 7.26% C) 9.23% D) 7.96%

B) r = (FV/PV)1/n - 1 = (35,571,000/80,000)1/87-1= 7.26

Median U.S. wages in 2014 were $53,675, compared to the median wage in 1990 of $28,960. What was the average annual increase in median wages over this 24-year period? A) 4.58% B) 2.60% C) 4.50% D) 1.31%

B) r=(FV/PV)1/n-1= (53,675/28,960)1/24= 2.60%

What annual rate of return must you earn to double your money in about 9 years? Use the Rule of 72 to determine your answer. A) You would need to earn an annual rate of return of about 12%. B) You would need to earn an annual rate of return of about 10%. C) You would need to earn an annual rate of return of about 8%. D) There is not enough information to answer this question.

C) 72/9=8

You wish to make a substantial down payment on a lake cottage and you currently have $15,725 invested at an annual rate of 2.50%. How much money will be in the account in 3.5 years if it continues to earn at its present rate? A) $18,325 B) $20,579 C) $17,144 D) $19,605

C) FV=PV*(1+r)^n= 15,725 *(1.025)^3.5 = 17,144

Andy would like to buy a new car but must complete a two-year commitment to the Peace Corp before he will drive the new car. The current price of the car Andy wants to buy is $32,000, and the dealer expects the price of a similar new car to be $35,000 in two years. If Andy can earn an annual interest rate of 4% on his money, should he buy the car now or wait for two years? Why? Note: Storage costs if Andy purchases the car are $0. Please limit your considerations to the factors offered in the answer choices. A) Andy is indifferent because his $32,000 investment will be worth exactly $35,000 after two years. B) Buy in two years because at $35,000 the car will cost less than the $36,385 Andy will have after investing the money for two years. C) Buy now because if Andy invests the $32,000 today it will only increase in value to $34,611, and this is less than the cost of his desired new car in two years. D) Buy in two years because $35,000 is a "real deal" for the car Andy wants.

C) FV=PV*(1+r)^n= 32,000 * (1.04)^2 = 34,611.20

If you invest $3,650 today, how much money will you have in 4 years? A) $3,650 B) $4,437 C) This question cannot be answered because it is missing an annual rate of return. D) This question cannot be answered because it is missing the type of investment made.

C) This question cannot be answered because it is missing an annual rate of return.

Drew is taking over as Chief Marketing Officer at SouthWest Foods. She has pledged to increase sales from their current level of $8,000,000 at a rate of 11% per year until the firm hits sales of $15,000,000 per year. How long will it take the firm to hit the target goal at this rate of increase? A) 5.18 years B) 5.36 years C) 6.02 years D) 7.62 years

C) n=ln(FV/PV) / ln(1+r)= ln(15,000,000/8,000,000) / ln(1.11)= 6.02

In 1975, the era of major league baseball free agency began. The average player salary was $16,000. In 1980, the average salary was $30,000. What was the average annual growth in the minimum salary in major league baseball over those five years? A) 5.92% B) 10.67% C) 13.40% D) 37.50%

C) r=(FV/PV)1/n-1= (30,000/16,000)1/5= 13.40%

In your first year out of college you hope to earn $30,000 per year. How many years will you have to work until you earn $120,000 if your income increases at a rate of 10% per year? Use the Rule of 72 to determine your answer. A) You would need to work for just over 7 years to reach an income level of $120,000 per year. B) You would need to work for just over 5 years to reach an income level of $120,000 per year. C) You would need to work for just over 14 years to reach an income level of $120,000 per year. D) You would need to work for just over 10 years to reach an income level of $120,000 per year.

C) 72/10= 7.2 years via the Rule of 72. to double to $60,000 and then another 7.2 years to double again to $120,000. This is a total of over 14 years

Your grandparents leave on their dream vacation to Antarctica in three years. The cruise vacation will cost them $24,000. If they have already saved $22,500 and are investing it at a rate of 2.50% per year, will they have saved enough money for their trip? A) No, to have enough money they would have already needed to save $23,375. B) Yes, to have enough money they would have already needed to save $22,101.33 and they already exceed that amount. C) No, because they forgot to factor in long underwear expenses. D) Yes, to have enough money they would have already needed to save $22,286.39 and they already exceed that amount.

D) PV = FV/(1+r)^n= $24,000/(1.025)^3= $22,286.39

You currently have $3,500 invested at an annual rate of 8%. How long will it take for this investment to grow to a value of $5,000? A) 5.00 years B) 4.37 years C) 5.60 years D) 4.63 years

D) n=ln(FV/PV) / ln(1+r)= ln(5,000/3,500) / ln(1.08)= 4.63%

Five years ago, Maria's annual salary was $73,500. Today, she earns $91,900. What has been the average annual percentage rate of growth of Maria's salary? A) 6.27% B) 8.89% C) $3,680 per year D) 4.57%

D) r = (FV/PV)1/n - 1 = (91,900/73,500)1/5-1= 4.57

You have saved $1,250 for a used motorcycle that has a current price of $1,550. If your money is sitting in an account earning 2.25% per year, how long will it take for this account to grow to $1,550? Note: The motorcycle's price may have changed by the time your account reaches a value of $1,550. A) 9.04 years B) 9.04 months C) 9.67 months D) 9.67 years

D) n=ln(FV/PV) / ln(1+r)= ln(1,550/1,250) / ln(1.0225)= 9.67

The question "How much will I have in my account at a specific point in the future, given a specific interest rate?" is best answered by which form of the TVM equation?

FV=PV × (1 + r)n

The current price on a 60-inch flat panel LCD HD television is $1,200. Big screen HD television prices have dropped at an average rate of 12% per year in recent years. If you expect this trend to continue, how much will this style of television cost in two years? A) $1,122 B) $1,087 C) $1,008 D) $929

FV=PV(1+r)^n = 1200 (1-0.12)^2 = D) $929.28

A manufacturer of Virtual Reality headsets has seen sales increase from 25,000 units per year to 100,000 units per year in 8 years. What has been the firm's average annual rate of increase in the number of television sets sold? Use the Rule of 72 to determine your answer. A) The average annual rate of change has been between 10% and 11%. B) The average annual rate of change has been between 18% and 19%. C) The average annual rate of change has been between 15% and 16%. D) There is not enough information to answer this question.

Unit sales doubled from 25,000 to 50,000 and doubled again to 100,000 in 8 years. Thus, at a doubling rate of every four years the Rule of 72 suggests an annual rate of 72/4 = 18%. Via the formula the actual growth rate is 18.92% per year.

The question "At what rate is my money growing over time?" is best answered by which form of the TVM equation?

r = (FV/PV)1/n - 1