Fin 300 Ch. 5 Liu

Suppose the first comic book of a classic series was sold in 1954. In 2015, the estimated price for this comic book in good condition was about $310,000. This represented a return of 22 percent per year. For this to be true, what was the original price of the comic book in 1954?

$ 1.67 PV = $ 310,000/(1 + .22)^61 -----> PV = $ 1.67

This morning, DJ's invested $238,000 to help fund a company expansion project planned for three years from now. How much additional money will the firm have three years from now if it can earn 4 percent rather than 3.5 percent on its savings?

$ 3,842.78 Future value = $238,000 ×(1 + .04)^3 = $267,717.63 Future value = $238,000 ×(1 + .035)^3 =$263,874.85 Difference = $267,717.63 - 263,874.85 = $3,842.78

Today, you earn a salary of $28,000. What will be your annual salary twelve years from now if you earn annual raises of 2.6 percent?

$ 38,100.12 Future value = $28,000 ×(1 + .026)12 = $38,100.12

You have just received notification that you have won the $1.25 million first prize in the Centennial Lottery. However, the prize will be awarded on your 100th birthday, 76 years from now. The appropriate discount rate is 6.8 percent. What is the present value of your winnings?

$ 8,423.54 PV = $ 1,250,000/(1.068)^76 = $ 8,423.54

For each of the following, compute the present value (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.): Present Value Years Interest Rate Future value $ ________________ 14 8% $ 15,151 _____________ 5 14% $ 48,557 ______________ 30 15% $ 883,073 ________________ 35 8% $ 547,164

5,158.33 --------- 25,218. 98 ---------- 12,337.10 --------- 37,007.19 ----------

Assume the average vehicle selling price in the United States last year was $35,996. The average price 4 years earlier was $29,208. What was the annual increase in the selling price over this time period?

5.36 % $ 35,996 = $ 29,208 ×(1 + r)^4 -----> r = 5.36 %

Solve for the unknown interest rate in each of the following (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.): Present Value Years Interest Rate Future value 290 3 $ 15,151 410 17 $ 48,557 44,000 18 $ 883,073 43,261 20 $ 547,164

5.96% ------- 6.74% ------ 9.05% ------ 11/61% ------

Assume the total cost of a college education will be $220,000 when your child enters college in 17 years. You presently have $60,000 to invest. What rate of interest must you earn on your investment to cover the cost of your child's college education?

7.94 % $ 220,000 = $ 60,000 (1 + r)^17 -----> r = 7.94 %

Which one of the following will produce the lowest present value interest factor? A.) 6 percent interest for 5 years. B.) 6 percent interest for 8 years. C.) 6 percent interest for 10 years. D.) 8 percent interest for 5 years. E.) 8 percent interest for 10 years

8 percent interest for 10 years.

Twelve years ago, your parents set aside $8,000 to help fund your college education. Today, that fund is valued at $23,902. What rate of interest is being earned on this account?

9.55 %

Solve for the unknown number of years in each of the following (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.): Present Value Years Interest Rate Future value 470 8% $ 987 720 12% $ 1,704 17,500 18% $ 275,671 20,600 14% $ 303,827

9.64 ----- 7.60 ----- 16.66 ------ 20.54 ------

On your ninth birthday, you received $300 which you invested at 4.5 percent interest, compounded annually. Your investment is now worth $756. How old are you today?

Age 30

Although appealing to more refined tastes, art as a collectible has not always performed so profitably. During 2003, an auction house sold a sculpture at auction for a price of $10,411,500. Unfortunately for the previous owner, he had purchased it in 1998 at a price of $12,577,500. What was his annual rate of return on this sculpture? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Annual rate of return: -3.71% CAGR: (Ending Value/Begining Value)^(1/n) -1

Which of these will increase the present value of an amount to be received sometime in the future? A.) Increase in the time until the amount is received. B.) Increase in the discount rate. C.) Decrease in the future value. D.) Decrease in the interest rate. E.) Decrease in both the future value and the number of time periods.

Decrease in the interest rate.

First City Bank pays 6 percent simple interest on its savings account balances, whereas Second City Bank pays 6 percent interest compounded annually. If you made a $72,000 deposit in each bank, how much more money would you earn from your Second City Bank account at the end of 10 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Difference in accounts: $ 13,741.03

In 1895, the first Putting Green Championship was held. The winner's prize money was $180. In 2014, the winner's check was $1,500,000. What was the percentage increase per year in the winner's check over this period? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Increase per year: 7.88%

Your grandmother has promised to give you $10,000 when you graduate from college. She is expecting you to graduate three years from now. What happens to the present value of this gift if you speed up your graduation by one year and graduate two years from now?

Increases.

What is the relationship between present value and future value interest factors?

The factors are reciprocals of each other.

In 1895, the first Putting Green Championship was held. The winner's prize money was $180. In 2014, the winner's check was $1,500,000. If the winner's prize increases at the same rate, what will it be in 2045? (Do not round intermediate calculations. Round your answer to 2 decimal places, e.g., 32.16.)

Winner's prize in 2045: $ 15,757,271.52