Finance Exam

QUESTIONS - Three questions below:

1) Answer the 3 sub-questions:  At an interest rate of 8 percent and using the Rule of 72, how long will it take to double the value of a lump sum invested today? How long will it take after that until the account grows to four times the initial investment? Given the power of compounding, shouldn't it take less time for the money to double the second time?

2) Answer the 2 sub-questions: What happens to the future value of an annuity if you increase the rate r? What happens to the present value?

3) Answer the 2 sub-questions:  You are considering two annuities, both of which pay a total of $20,000 over the life of the annuity. Annuity A pays $2,000 at the end of each year for the next 10 years. Annuity B pays $1,000 at the end of each year for the next 20 years. Which annuity has the greater value today? Is there any circumstance where the two annuities would have equal values as of today? Explain.

PROBLEMS - 18 questions below

1) You have just received notification that you have won the $3.5 million first prize in the Centennial Lottery. However, the prize will be awarded on your 100th birthday, 78 years from now. The appropriate discount rate is 7 percent (compounded annually). What is the present value of your winnings?

2) On your tenth birthday, you received $500 which you invested at 9.5 percent interest, compounded annually. Your investment is now worth $2500. How old are you today? 

3) You expect to receive $8,000 at graduation in 4 years. You plan on investing this money at 10 percent (compounded annually) until you have $60,000. How many years will it be until this occurs?

4) Sean invested $2,000 in an account that pays 10 percent simple interest. How much more money could Sean have earned at the end of ten years if the 10 percent interest had compounded annually?

5) You have just made a $1,500 contribution to your individual retirement account. Assume you earn a 11 percent rate of return (compounded annually) and make no additional contributions. How much more will your account be worth when you retire in 25 years than it would be if you waited another 10 years before making this contribution (what is difference of FVs 25 years from now versus the FV if wait 10 years)?

6) Assume the total cost of a college education will be $250,000 when your child enters college in 15 years. You presently have $50,000 to invest. What rate of interest must you earn on your investment to cover the cost of your child's college education?

7) You're trying to save to buy a new $50,000 Audi. You have $10,000 today that can be invested at your bank. The bank pays 6.5 percent annual interest (compounded annually) on its accounts. How many years will it be before you have enough to buy the car? Assume the price of the car remains constant.

8) What is the future value of annual payments of $10,000 a year for 15 years at 10 percent interest compounded annually?

9) Your older sister deposited $5,000 today at 6 percent interest for 5 years. You would like to have just as much money at the end of the next 5 years as your sister will have. However, you can only earn 4 percent interest. How much more money must you deposit today than your sister did if you are to have the same amount at the end of the 5 years?

10) Common Bank wants to appear competitive based on quoted loan rates and thus must offer a 10.35 percent annual percentage rate (APR) on its loans. What is the maximum rate the bank can actually earn based on the quoted rate?

11) Seasoned Bank wants to earn an effective annual return on its consumer loans of 8.85 percent per year. The bank uses daily compounding on its loans. By law, what interest rate is the bank required to report to potential borrowers?

12) Your employer contributes $150 a week to your retirement plan. Assume that you work for your employer for another 20 years and that the rate of return is 5 percent compounded weekly. Given these assumptions, what is this employee benefit worth to you in 20 years?

13) Sue can afford $500 a month for 3 years for a car loan. If the interest rate is 4 percent compounded monthly, how much can he afford today to borrow to purchase a car?

14) You are scheduled to receive annual payments of $5,100 for each of the next 7 years. The discount rate is 7 percent compounded annually. What is the difference in the present value if you receive these payments at the beginning of each year (Annuity due) rather than at the end of each year (Ordinary Annuity)?

15) You are borrowing $15,000 to buy a car. The terms of the loan call for monthly payments for 5 years at 4.5 percent interest compounded monthly. What is the amount of each monthly payment?

16) Alexa plans on saving $2,000 a year and expects to earn an annual rate of 12 percent compounded annually. How much will she have in her account at the end of 40 years?

17) You are paying an Effective annual rate of 20.689 percent on your credit card. The interest is compounded monthly. What is the annual percentage rate (nominal rate) on this account?

18) A preferred stock pays an annual dividend of $3.50 (this is a Perpetuity). What is one share of this stock worth today if the rate of return is 12 percent?

MULTIPLE CHOICE QUESTIONS -

1) You are comparing two annuities which offer quarterly payments of $2,500 for five years and pay 0.75 percent interest per month. Annuity A will pay you on the first of each month while annuity B will pay you on the last day of each month. Which one of the following statements is correct concerning these two annuities?

A. These two annuities have equal present values but unequal futures values at the end of year five.

B. These two annuities have equal present values as of today and equal future values at the end of year five.

C. Annuity B is an annuity due.

D. Annuity A has a smaller future value than annuity B.

E. Annuity B has a smaller present value than annuity A.

2) Which of the following statements related to interest rates are correct?

I. Annual interest rates consider the effect of interest earned on reinvested interest payments.

II. When comparing loans, you should compare the effective annual rates.

III. Lenders are required by law to disclose the effective annual rate of a loan to prospective borrowers.

IV. Annual and effective interest rates are equal when interest is compounded annually.

A. I and II only

B. II and III only

C. II and IV only

D. I, II, and III only

E. II, III, and IV only

3) You are investing $100 today in a savings account at your local bank. Which one of the following terms refers to the value of this investment one year from now?

A. future value

B. present value

C. principal amounts

D. discounted value

E. invested principal

4) An ordinary annuity is best defined by which one of the following?

A. increasing payments paid for a definitive period of time

B. increasing payments paid forever

C. equal payments paid at regular intervals over a stated time period

D. equal payments paid at regular intervals of time on an ongoing basis

E. unequal payments that occur at set intervals for a limited period of time

5) The process of determining the present value of future cash flows in order to know their worth today is called which one of the following?

A. compound interest valuation

B. interest on interest computation

C. discounted cash flow valuation

D. present value interest factoring

E. complex factoring

6) You are considering two loans. The terms of the two loans are equivalent with the exception of the interest rates. Loan A offers a rate of 7.75 percent, compounded daily. Loan B offers a rate of 8 percent, compounded semi-annually. Which loan should you select and why?

A. A; the effective annual rate is 8.06 percent.

B. A; the annual percentage rate is 7.75 percent.

C. B; the annual percentage rate is 7.68 percent.

D. B; the effective annual rate is 8.16 percent.

E. The loans are equivalent offers so you can select either one.

7) Today, you are retiring. You have a total of $411,016 in your retirement savings and have the funds invested such that you expect to earn an average of 7.10 percent, compounded monthly, on this money throughout your retirement years. You want to withdraw $2,500 at the beginning of every month, starting today. How long will it be until you run out of money?

A. 31.97 years

B. 34.56 years

C. 42.03 year

D. 48.19 years

E. You will never run out of money.

BONUS QUESTIONS BELOW:

BONUS Question 1) You are considering between two mutual fund investment portfolios. The strategy of the two funds are similar with the exception of the most recent annual rate of return. Fund A has a rate of return of 10.75 percent, compounded daily. Fund B has a rate of return of 11.25 percent, compounded monthly. Which Fund should you select and why?

BONUS Question 2) What is the present value of $10,500 per year, at a discount rate of 10 percent if the first payment is received 10 years from now and the last payment is received 30 years from now?

BONUS Question 3) Problem Case: This is a classic retirement problem. A time line will help in solving it. Your friend is celebrating her 35th birthday today and wants to start saving for her anticipated retirement at age 65. She wants to be able to withdraw $105,000 from her savings account on each birthday for 20 years following her retirement; the first withdrawal will be on her 66th birthday. Your friend intends to invest her money in the local credit union, which offers 7 percent interest per year. She wants to make equal annual payments on each birthday into the account established at the credit union for her retirement fund.

Question - Suppose your friend's employer will contribute $3,500 to the account every year as part of the company's profit-sharing plan. In addition, your friend expects a $175,000 distribution from a family trust fund on her 55th birthday, which she will also put into the retirement account. What amount must she deposit annually now to be able to make the desired withdrawals at retirement?

Attachment:- Assignment File.rar