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Exam 5: Time Value of Money

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Question 41

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Which of the following statements is CORRECT?

A) The cash flows for an ordinary (or deferred) annuity all occur at the beginning of the periods.
B) If a series of unequal cash flows occurs at regular intervals, such as once a year, then the series is by definition an annuity.
C) The cash flows for an annuity due must all occur at the beginning of the periods.
D) The cash flows for an annuity may vary from period to period, but they must occur at regular intervals, such as once a year or once a month.
E) If some cash flows occur at the beginning of the periods while others occur at the ends, then we have what the textbook defines as a variable annuity.

F) A) and B)
G) C) and D)

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Question 42

Multiple Choice

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Assume that you own an annuity that will pay you $15,000 per year for 12 years, with the first payment being made today. You need money today to start a new business, and your uncle offers to give you $120,000 for the annuity. If you sell it, what rate of return would your uncle earn on his investment?

A) 6.85%
B) 7.21%
C) 7.59%
D) 7.99%
E) 8.41%

F) A) and B)
G) A) and C)

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Question 43

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All other things held constant, the present value of a given annual annuity decreases as the number of periods per year increases.

You want to quit your job and go back to school for a law degree 4 years from now, and you plan to save $3,500 per year, beginning immediately. You will make 4 deposits in an account that pays 5.7% interest. Under these assumptions, how much will you have 4 years from today?

Suppose you are buying your first condo for $145,000, and you will make a $15,000 down payment. You have arranged to finance the remainder with a 30-year, monthly payment, amortized mortgage at a 6.5% nominal interest rate, with the first payment due in one month. What will your monthly payments be?

How much would $100, growing at 5% per year, be worth after 75 years?

Suppose you inherited $275,000 and invested it at 8.25% per year. How much could you withdraw at the beginning of each of the next 20 years?

Your sister turned 35 today, and she is planning to save $7,000 per year for retirement, with the first deposit to be made one year from today. She will invest in a mutual fund that's expected to provide a return of 7.5% per year. She plans to retire 30 years from today, when she turns 65, and she expects to live for 25 years after retirement, to age 90. Under these assumptions, how much can she spend each year after she retires? Her first withdrawal will be made at the end of her first retirement year.

Master Card and other credit card issuers must by law print the Annual Percentage Rate (APR) on their monthly statements. If the APR is stated to be 18.00%, with interest paid monthly, what is the card's EFF%?

Which of the following statements is CORRECT?

What is the present value of the following cash flow stream at a rate of 12.0%?

You want to buy a new ski boat 2 years from now, and you plan to save $8,200 per year, beginning one year from today. You will deposit your savings in an account that pays 6.2% interest. How much will you have just after you make the 2nd deposit, 2 years from now?

If the discount (or interest) rate is positive, the future value of an expected series of payments will always exceed the present value of the same series.

Time lines can be constructed in situations where some of the cash flows occur annually but others occur quarterly.

You inherited an oil well that will pay you $25,000 per year for 25 years, with the first payment being made today. If you think a fair return on the well is 7.5%, how much should you ask for it if you decide to sell it?

Riverside Bank offers to lend you $50,000 at a nominal rate of 6.5%, compounded monthly. The loan (principal plus interest) must be repaid at the end of the year. Midwest Bank also offers to lend you the $50,000, but it will charge an annual rate of 7.0%, with no interest due until the end of the year. How much higher or lower is the effective annual rate charged by Midwest versus the rate charged by Riverside?

What is the present value of the following cash flow stream at a rate of 6.25%?

You are considering two equally risky annuities, each of which pays $5,000 per year for 10 years. Investment ORD is an ordinary (or deferred) annuity, while Investment DUE is an annuity due. Which of the following statements is CORRECT?

You are considering an investment in a Third World bank account that pays a nominal annual rate of 18%, compounded monthly. If you invest $5,000 at the beginning of each month, how many months would it take for your account to grow to $250,000? Round fractional months up.

You deposit $1,000 today in a savings account that pays 3.5% interest, compounded annually. How much will your account be worth at the end of 25 years?