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Exam 5: Time Value of Money

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Question 31

Multiple Choice

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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 E)
G) A) and B)

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Question 32

Multiple Choice

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Your bank offers to lend you $100,000 at an 8.5% annual interest rate to start your new business. The terms require you to amortize the loan with 10 equal end-of-year payments. How much interest would you be paying in Year 2?

A) $7,531
B) $7,927
C) $8,323
D) $8,740
E) $9,177

F) B) and E)
G) A) and E)

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Question 33

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A time line is not meaningful unless all cash flows occur annually.

Janice has $5,000 invested in a bank that pays 3.8% annually. How long will it take for her funds to triple?

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?

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?

Sam was injured in an accident, and the insurance company has offered him the choice of $25,000 per year for 15 years, with the first payment being made today, or a lump sum. If a fair return is 7.5%, how large must the lump sum be to leave him as well off financially as with the annuity?

Suppose Community Bank offers to lend you $10,000 for one year at a nominal annual rate of 8.00%, but you must make interest payments at the end of each quarter and then pay off the $10,000 principal amount at the end of the year. What is the effective annual rate on the loan?

If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by multiplying the periodic rate by the number of periods per year.

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

What's the present value of $4,500 discounted back 5 years if the appropriate interest rate is 4.5%, compounded semiannually?

Charter Bank pays a 4.50% nominal rate on deposits, with monthly compounding. What effective annual rate (EFF%) does the bank pay?

Suppose an Exxon Corporation bond will pay $4,500 ten years from now. If the going interest rate on safe 10-year bonds is 4.25%, how much is the bond worth today?

A $50,000 loan is to be amortized over 7 years, with annual end-of-year payments. Which of these statements is CORRECT?

Which of the following statements regarding a 15-year (180-month) $125,000, fixed-rate mortgage is CORRECT? (Ignore taxes and transactions costs.)

The payment made each period on an amortized loan is constant, and it consists of some interest and some principal. The closer we are to the end of the loan's life, the smaller the percentage of the payment that will be a repayment of principal.

As a result of compounding, the effective annual rate on a bank deposit (or a loan) is always equal to or greater than the nominal rate on the deposit (or loan).

The present value of a future sum increases as either the discount rate or the number of periods per year increases, other things held constant.

Time lines can be constructed for annuities where the payments occur at either the beginning or the end of the periods.

A time line is meaningful even if all cash flows do not occur annually.