Question 1

When a loan is amortized over a five year term, the:

Accepted Answer

When a loan is amortized over a five year term, the amount of interest paid is reduced each year because the payments are structured to pay off both the principal and the interest over the term of the loan. As the principal balance decreases, the amount of interest charged on that balance also decreases. The rate of interest and payment may remain constant throughout the term of the loan. There is no balloon payment in this scenario because the loan is fully paid off over the five year term. Therefore, option B is the best choice.

Question 2

The effective rate of interest will always be ____ the nominal rate.

Accepted Answer

The effective rate of interest takes into account the compounding effect within a given period, which can make it equal to or greater than the nominal rate, depending on the frequency of compounding.

Question 3

The ____ of a resource is the benefit that would have been available from its next best use.

Accepted Answer

Opportunity cost is the benefit that could have been gained from the next best alternative use of a resource. Present value and future value refer to the current and future worth of an investment, respectively, and are not related to the concept of opportunity cost.

Question 4

When using a present value of an annuity table:

Accepted Answer

Option B is correct because as the interest rate increases, the present value of the annuity decreases, resulting in a decrease in the PVFA factor. Option C is also correct because as the number of periods increases, the present value of the annuity increases, resulting in an increase in the PVFA factor. Option A is incorrect because it depends on whether the payments are assumed to be made at the beginning of each period or at the end of each period, but the question does not specify which one is being used.

Question 5

The more frequent the compounding the:

Accepted Answer

The more frequent the compounding, the greater the effective interest rate, because the interest is being added more often throughout the year. This can lead to significantly higher returns over time. Therefore, choice C is the correct answer. Choices A, B, and D are not accurate, since they do not reflect the impact of compounding frequency on returns.

Question 6

If a series of equal payments is paid regularly out of a bank account which earns a constant rate of interest, the ____ is the amount that must be in the bank at the beginning of the series to just fund all of the payments.

Accepted Answer

The present value of an ordinary annuity represents the amount needed at the beginning of the series to fund all of the payments at a given interest rate. The future value of an annuity due represents the total amount of the payments plus interest at the end of the series when payments are made at the beginning of each period. Therefore, option D is the correct choice.

Question 7

A(n)____ is a financial instrument that agrees to pay an equal amount of money per period into the indefinite future (i.e. forever).

Accepted Answer

A perpetuity is a type of financial instrument that agrees to pay an equal amount of money per period into the indefinite future. It differs from an ordinary annuity, which has a set period of time for payments. Examples of perpetuities include bonds that have no maturity date and stocks that pay a fixed dividend indefinitely.

Question 8

Interest rates are quoted by stating the ____ followed by the compounding period.

Accepted Answer

Nominal rate is the stated rate of interest, which is typically quoted on an annual basis. The compounding period refers to how often the interest is added to the principal, such as annually, semi-annually, quarterly, or monthly. Therefore, interest rates are quoted by stating the nominal rate followed by the compounding period (e.g. 6% annually compounded quarterly).

Question 9

How much must be invested today to have $1,000 in two years if the interest rate is 5%?

Accepted Answer

The answer of How much must be invested today to...

Question 10

If a series of equal payments is received regularly at the end of the year, and each is deposited immediately at the same interest rate, the ____ is the sum of all the payments and all the interest earned at the end of the series.

Accepted Answer

The scenario described is that of a future value of an ordinary annuity calculation, where the payments are received at the end of each period and there is interest earned on each payment. The future value of the annuity is the accumulated amount of all payments plus the interest earned on each payment at the end of the series. The other options, such as present value of an annuity due or future value of an annuity due, do not accurately describe the scenario given in the question.

Question 11

The present value of an annuity will be decreased by:

Accepted Answer

The answer of The present value of an annuity will...

Question 12

What is the rate of return on an investment if you lend $1,000 and are repaid $1,254.70 two years later?

Accepted Answer

The rate of return can be calculated using the formula for compound interest: A = P(1 + r)^n, where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate, and n is the time the money is invested for in years. Rearranging the formula to solve for r gives us r = [(A/P)^(1/n)] - 1. Substituting the given values (A = $1,254.70, P = $1,000, n = 2 years) gives us r = [(1254.70/1000)^(1/2)] - 1 = 0.12, or 12%.

Question 13

The annual effective rate of interest is a function of:

Accepted Answer

The annual effective rate of interest is calculated based on the annual nominal rate of interest and the number of compounding intervals per year. Therefore, both options A and B are necessary to determine the annual effective rate of interest. Option C, the imbedded annuity, is not relevant in this calculation.

Question 14

Which of the following is most correct?

Accepted Answer

An annuity due has payments at the beginning of each period, so its present and future values are higher than those of an ordinary annuity, where payments are made at the end of each period.

Question 15

If the interest rate is 6%, which expression will determine the appropriate price to pay for a business that you expect to earn $5,000 in each of the next ten years and be sold for $25,000 in the eleventh year.

Accepted Answer

The correct expression uses the Present Value of an Annuity formula (PVFA) for the $5,000 annual earnings over 10 years and the Present Value formula (PVF) for the $25,000 to be received in the 11th year, both discounted at a 6% interest rate.

Question 16

Find the present value of $100 to be received at the end of two years if the discount rate is 12% compounded monthly.

Accepted Answer

The present value (PV) is calculated using the formula: $ PV = \frac{FV}{(1 + r/n)^{nt}} $, where $ FV = 100 $, $ r = 0.12 $, $ n = 12 $, and $ t = 2 $. Plugging in these values gives $ PV = \frac{100}{(1 + 0.12/12)^{12 \times 2}} \approx 78.76 $.

Question 17

More frequent compounding results in ____ future values and ____ present values than less frequent compounding at the same nominal interest rate.

Accepted Answer

More frequent compounding increases the future value because interest is being added to the principal more often, allowing interest to be earned on interest more frequently. However, it results in lower present values because a given future amount discounts to a smaller present value when interest is compounded more frequently at the same nominal rate.

Question 18

You have just won a $5 million lottery to be received in twenty annual equal payments of $250,000. What will happen to the present value of your winnings if the interest rate increases?

Accepted Answer

An increase in interest rate will result in a decrease in present value of the winnings. This is because the future cash flows (the twenty annual payments) are worth less in today's dollars when discounted at a higher interest rate.

Question 19

Which of the following phrases would not be utilized if the payments were an annuity due?

Accepted Answer

An annuity due involves payments at the beginning of each period, so "End-of-period payments" would not be used to describe it, as this phrase implies payments are made at the end of each period, which is characteristic of an ordinary annuity, not an annuity due.

Question 20

A series of equal payments that occur at equal intervals and go on forever is called a(n):

Accepted Answer

A perpetuity is a series of equal payments that occur at equal intervals and go on forever. The other options have different characteristics: an ordinary annuity has a finite number of payments, an annuity due has payments that occur at the beginning instead of the end of each period, and a non-ending stream is not a commonly used financial term.

Quiz 6: Time Value of Money