finance problems
21. Today is your birthday, and you decide to start saving for your college education. You will begin college on your 18th birthday and will need $4,000 per year at the end of each of the following 4 years. You will make a deposit one year from today in an account paying 12 percent annually and continue to make an identical deposit each year up to and including the year you begin college. If a deposit amount of $2,542.05 will allow you to reach your goal, what birthday are you celebrating today?
a. 13 b. 14 c. 15 d. 16 e. 17
22. Assume that your aunt sold her house on December 31 and that she took a mortgage in the amount of $10,000 as part of the payment. The mortgage has a simple interest rate of 10 percent, but it calls for payments every 6 months, beginning on June 30, and the mortgage is to be amortized over 10 years. Now, one year later, your aunt must file Schedule B of her tax return with the IRS informing them of the interest that was included in the two payments made during the year. (This interest will be income to your aunt and a deduction to the buyer of the house.) What is the total amount of interest that was paid during the first year?
a. $1,604.86 b. $619.98 c. $984.88 d. $1,205.76 e. $750.02
23. Assume that you inherited some money. A friend of yours is working as an unpaid intern at a local brokerage firm, and her boss is selling some securities that call for four payments, $50 at the end of each of the next 3 years, plus a payment of $1,050 at the end of Year 4. Your friend says she can get you some of these securities at a cost of $900 each. Your money is now invested in a bank that pays an 8 percent simple interest rate, but with quarterly compounding. You regard the securities as being just as safe, and as liquid, as your bank deposit, so your required effective annual rate of return on the securities is the same as that on your bank deposit. You must calculate the value of the securities to decide whether they are a good investment. What is their present value to you?
a. $957.75 b. $888.66 c. $923.44 d. $1,015.25 e. $893.26
24. Your company is planning to borrow $1,000,000 on a 5year, 15 percent, annual payment, fully amortized term loan. What fraction of the payment made at the end of the second year will represent repayment of principal?
a. 57.18% b. 42.82% c. 50.28% d. 49.72% e. 60.27%
25. Your firm can borrow from its bank for one month. The loan will have to be “rolled over” at the end of the month, but you are sure the rollover will be allowed. The simple interest rate is 14 percent, but interest will have to be paid at the end of each month, so the bank interest rate is 14 percent, monthly compounding. Alternatively, your firm can borrow from an insurance company at a simple interest rate that would involve quarterly compounding. What simple quarterly rate would be equivalent to the rate charged by the bank?
a. 12.44% b. 14.16% c. 13.55% d. 13.12% e. 12.88%
26. Assume that you have $15,000 in a bank account that pays 5 percent annual interest. You plan to go back to school for a combination MBA/law degree 5 years from today. It will take you an additional 5 years to complete your graduate studies. You figure you will need a fixed income of $25,000 in today’s dollars; that is, you will need $25,000 of today’s dollars during your first year and each subsequent year. (Thus, your real income will decline while you are in school.) You will withdraw funds for your annual expenses at the beginning of each year. Inflation is expected to occur at the rate of 3 percent per year. How much must you save during each of the next 5 years in order to achieve your goal? The first increment of savings will be deposited one year from today.
a. $20,241.66 b. $19,224.55 c. $18,792.11 d. $19,559.42 e. $20,378.82
27. You plan to buy a new HDTV. The dealer offers to sell the set to you on credit. You will have 3 months in which to pay, but the dealer says you will be charged a 15 percent interest rate; that is, the simple interest rate is 15 percent, quarterly compounding. As an alternative to buying on credit, you can borrow the funds from your bank, but the bank will make you pay interest each month. At what simple bank interest rate should you be indifferent between the two types of credit?
a. 13.7643% b. 14.2107% c. 14.8163% d. 15.5397% e. 15.3984%
28. Assume that your father is now 50 years old, that he plans to retire in 10 years, and that he expects to live for 25 years after he retires, that is, until he is 85. He wants a fixed retirement income that has the same purchasing power at the time he retires as $60,000 has today (he realizes that the real value of his retirement income will decline yearbyyear after he retires). His retirement income will begin the day he retires, 10 years from today, and he will then get 24 additional annual payments. Inflation is expected to be 5 percent per year from today forward; he currently has $150,000 saved; and he expects to earn a return on his savings of 7 percent per year, annual compounding. To the nearest dollar, how much must he save during each of the next 10 years (with deposits being made at the end of each year) to meet his retirement goal?
a. $66,847.95 b. $77,201.21 c. $54,332.88 d. $41,987.33 e. $62,191.25
29. A rookie quarterback is in the process of negotiating his first contract. The team’s general manager has offered him three possible contracts. Each of the contracts lasts for four years. All of the money is guaranteed and is paid at the end of each year. The payment terms of the contracts are listed below:
Year Contract 1 Contract 2 Contract 3
1 $1.5 million $1.0 million $3.5 million
2 1.5 million 1.5 million 0.5 million
3 1.5 million 2.0 million 0.5 million
4 1.5 million 2.5 million 0.5 million
The quarterback discounts all cash flows at 12 percent. Which of the three contracts offers the most value?
a. Contract 1; its present value is $4.56 million.
b. Contract 2; its present value is $5.10 million.
c. Contract 3; its present value is $4.20 million.
d. Either Contract 2 or Contract 3; each provides a present value of $5.10 million.
e. Either Contract 1 or Contract 2; each provides a present value of $5.10 million.

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Solution: finance problems