Question 1

What is the relationship between the present value factor of an ordinary annuity and the present value factor of an annuity due for the same interest rate?

Accepted Answer

The present value factor of an annuity due is always greater than the present value factor of an ordinary annuity for the same interest rate and time periods. Specifically, the annuity due factor equals one plus the ordinary annuity factor for n periods. Therefore, choice B is correct. The other choices are incorrect.

Question 2

Which of the following statements is false?

Accepted Answer

The factor for the present value of an annuity due is found by multiplying the ordinary annuity table value by one plus the interest rate, not one minus the interest rate.

Question 3

Jerry recently was offered a position with a major accounting firm. The firm offered Jerry either a signing bonus of $23,000 payable on the first day of work or a signing bonus of $26,000 payable after one year of employment. Assuming that the relevant interest rate is 10%, which option should Jerry choose?

Accepted Answer

To compare the two options, we need to bring their values to the same point in time. The relevant interest rate is 10%, which means that the future value of $23,000 after one year is:

FV = PV x (1 + r)
FV = $23,000 x (1 + 0.10)
FV = $25,300

So if Jerry takes the $23,000 upfront, he could invest it for one year at 10% and have $25,300 at the end of the year. Therefore, the option to take $26,000 after one year of employment is better since it provides a higher amount at that point in time.

Question 4

Assume ABC Company deposits $70,000 with First National Bank in an account earning interest at 6% per annum, compounded semi-annually. How much will ABC have in the account after five years if interest is reinvested?

Accepted Answer

The future value of an investment compounded semi-annually is calculated using the formula A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. Plugging in the values: A = $70,000(1 + 0.06/2)^(2*5) = $70,000(1 + 0.03)^(10) = $70,000(1.03)^10 ≈ $94,074.

Question 5

Which of the following statements is true?

Accepted Answer

Option C is true as it represents the concept of present value and how it is affected by compounding interest rates. The higher the interest rate, the lower the present value. Option A is incorrect as it suggests an inverse relationship between the discount rate and present value. Option B is also incorrect as the process of accumulating interest on interest is referred to as compounding, not discounting. Option D is incorrect as the present value of a single sum increases as the date draws closer to the due date, as the time value of money decreases.

Question 6

Stemway Company requires a new manufacturing facility. It found three locations; all of which would provide the needed capacity, the only difference is the price. Location A may be purchased for $500,000. Location B may be acquired with a down payment of $100,000 and annual payments at the end of each of the next twenty years of $50,000. Location C requires $40,000 payments at the beginning of each of the next twenty-five years. Assuming Stemway's borrowing costs are 8% per annum, which option is the least costly to the company?

Accepted Answer

To determine the least costly option, we need to calculate the present value (PV) of each option using the given borrowing cost of 8% per annum as the discount rate. - For Location A, the cost is straightforward: $500,000.- For Location B, we use the formula for the present value of an annuity because it involves equal payments at the end of each period. The PV formula for an annuity is PV = P * [(1 - (1 + r)^-n) / r], where P is the payment, r is the interest rate per period, and n is the number of periods. The down payment is made today, so its present value is simply $100,000. The annuity's present value is the $50,000 annual payments for 20 years at 8%, which calculates to approximately $500,840. Adding the down payment, the total PV is about $600,840.- For Location C, since payments are made at the beginning of each period, it's considered an annuity due. The formula for the present value of an annuity due is PV = P * [(1 - (1 + r)^-n) / r] * (1 + r), where P, r, and n have the same meanings. The present value of $40,000 payments at the beginning of each of the next 25 years at 8% calculates to approximately $449,678.Comparing the present values, Location C is the least costly option for Stemway Company.

Question 7

Present value is

Accepted Answer

Present value is the value now of a future amount, the amount that must be invested now to produce a known future value, and is always smaller than the future value. Therefore, all of these answer choices are correct.

Question 8

Which of the following is false?

Accepted Answer

The answer of Which of the following is false?
...

Question 9

If the number of periods is known, the interest rate is determined by

Accepted Answer

To find the interest rate when the number of periods is known, you divide the future value by the present value and look for the quotient in the future value of 1 table.

Question 10

If Jethro wanted to save a set amount each month in order to buy a new pick-up truck when the new models are next available, which time value concept would be used to determine the monthly payment?

Accepted Answer

Jethro wants to save a set amount each month, which indicates a regular payment over a certain period. Therefore, the concept of the future value of an ordinary annuity would be used to determine the monthly payment needed to achieve his goal of buying a new pick-up truck in the future.

Question 11

If an annuity due and an ordinary annuity have the same number of equal payments and the same interest rates, then

Accepted Answer

CAn annuity due involves payments at the beginning of each period, while an ordinary annuity involves payments at the end. For the present value, payments made sooner (as in an annuity due) are worth more today due to the time value of money, making the present value of an annuity due greater than that of an ordinary annuity. For the future value, both types of annuities will have different future values due to the timing of payments, but the statement C is incorrect as it suggests equality; the correct relationship is that the future value of an annuity due is greater because payments have more time to earn interest. However, since this specific comparison was not an option, the correct understanding is that their future values are not equal, with the annuity due generally having a higher future value.

Question 12

An accountant wishes to find the present value of an annuity of $1 payable at the beginning of each period at 10% for eight periods. The accountant has only one present value table which shows the present value of an annuity of $1 payable at the end of each period. To compute the present value, the accountant would use the present value factor in the 10% column for

Accepted Answer

The correct approach is to use the present value factor for eight periods and then multiply by (1 + .10) because the payments are made at the beginning of each period, effectively moving the entire annuity one period forward in time, which is equivalent to multiplying by (1 + the interest rate).

Question 13

Which of the following is true?

Accepted Answer

In an annuity due, rents occur at the beginning of each period, while in an ordinary annuity, rents occur at the end of each period. Therefore, option C is the correct statement.

Question 14

Sue Gray wants to invest a certain sum of money at the end of each year for five years. The investment will earn 6% compounded annually. At the end of five years, she will need a total of $40,000 accumulated. How should she compute her required annual invest-ment?

Accepted Answer

To find the required annual investment to accumulate a future sum, you divide the future sum by the future value of an ordinary annuity factor. This gives you the annual amount needed to invest to reach the desired future value, considering the interest rate and time period.

Question 15

Al Darby wants to withdraw $20,000 (including principal) from an investment fund at the end of each year for five years. How should he compute his required initial investment at the beginning of the first year if the fund earns 10% compounded annually?

Accepted Answer

To find the required initial investment, we need to calculate the present value of an annuity that pays $20,000 annually for five years at a 10% annual interest rate. This can be done using the formula for the present value of an ordinary annuity:
PV = PMT x [1 - (1+r)^-n] / r
where PV is the present value, PMT is the annuity payment, r is the interest rate, and n is the number of periods.
Substituting the values, we get:
PV = $20,000 x [1 - (1+0.10)^-5] / 0.10
PV = $20,000 x [1 - 0.6209] / 0.10
PV = $20,000 x 3.791
PV = $75,820.61
Therefore, the required initial investment at the beginning of the first year is $75,820.61, which is option C.

Question 16

What is the primary difference between an ordinary annuity and an annuity due?

Accepted Answer

The primary difference between an ordinary annuity and an annuity due is the timing of the periodic payment. In an ordinary annuity, payments are made at the end of each period, while in an annuity due, payments are made at the beginning of each period. This difference can impact the present and future value calculations of the annuity.

Question 17

What is the relationship between the future value of one and the present value of one?

Accepted Answer

The present value of one is calculated by dividing one by the future value of one, reflecting the concept that a dollar today is worth more than a dollar in the future due to the potential earning capacity. This relationship is fundamental in finance, illustrating how money's value decreases over time when considering its future earning potential.

Question 18

Peter invests $100,000 in a 3-year certificate of deposit earning 3.5% at his local bank. Which time value concept would be used to determine the maturity value of the certificate?

Accepted Answer

The future value of one concept is used to calculate how much a single sum of money today will grow to at a future date given a specific interest rate, which is exactly what is needed to determine the maturity value of a certificate of deposit.

Question 19

An amount is deposited for eight years at 8%. If compounding occurs quarterly, then the table value is found at

Accepted Answer

Since the interest is compounded quarterly, the rate per period is 8%/4 = 2% and the number of periods over eight years is 8*4 = 32.

Question 20

Paula purchased a house for $300,000. After providing a 20% down payment, she borrowed the balance from the local savings and loan under a 30-year 6% mortgage loan requiring equal monthly installments at the end of each month. Which time value concept would be used to determine the monthly payment?

Accepted Answer

The monthly payment is determined by calculating the present value of the loan amount, which is the present value of an ordinary annuity.

Quiz 6: Accounting and the Time Value of Money