Question 1

The present value of $2,000 to be received nine years from today at 8% interest compounded annually is $1,000.
Calculation: $2,000 x 0.5002 = $1,000.

Accepted Answer

The present value formula for compound interest is:
Present value = Future value ÷ (1 + interest rate)^n, 
where n is the number of years. 
Using this formula, we can solve for the interest rate:
$1,000 = $2,000 ÷ (1 + interest rate)^9
(1 + interest rate)^9 = 2
1 + interest rate = 2^(1/9)
interest rate = 2^(1/9) - 1
interest rate = 0.079 = 7.9%
So, the interest rate is not 8%, but 7.9%. 
However, the present value calculation given is correct:
$2,000 x 0.5002 = $1,000
Therefore, the answer is A, true.

Question 2

Interest is the payment to the owner of an asset for its use by a borrower.

Accepted Answer

This is the definition of interest. It is the compensation paid by a borrower to the owner of an asset for using it.

Question 3

An ordinary annuity refers to a series of equal payments made or received at the end of each period.

Accepted Answer

An ordinary annuity involves payments made or received at the end of each period. This is in contrast to an annuity due, which involves payments made or received at the beginning of each period.

Question 4

The present value of 1 formula is often useful when a borrowed asset must be repaid in full at a later date and the borrower wants to know its worth at the future date.

Accepted Answer

The present value of 1 formula is used to determine the current worth of a future sum of money, not its worth at a future date.

Question 5

The present value factor for determining the present value of $6,300 to be received three years from today at 10% interest compounded semiannually is 0.7462.

Accepted Answer

The present value factor for determining the present value of $6,300 to be received three years from today at 10% interest compounded semiannually is calculated as follows:

n = number of periods = 6 (since interest is compounded semiannually, there are 2 periods per year for 3 years)
i = interest rate per period = 10%/2 = 5%
PVF = (1 + i)^-n = (1 + 0.05)^-6 = 0.7462

Therefore, the statement is true.

Question 6

The present value of an annuity table can be used to determine the series of equal payments that are required by a loan agreement.

Accepted Answer

The present value of an annuity table provides the present value of a series of equal payments, which can be used to determine the size of the payments required by a loan agreement.

Question 7

Future value can be found if the interest rate (i), the number of periods (n), and the present value (p) are known.

Accepted Answer

This is true according to the formula for future value, which is FV = P(1+i)^n.

Question 8

The number of periods in a present value calculation can only be expressed in years.

Accepted Answer

The number of periods in a present value calculation can be expressed in any time unit (days, weeks, months, etc.) as long as the interest rate is adjusted accordingly.

Question 9

In a present value or future value table, the length of one time period may be interpreted as one year, one month, or any other length of time.

Accepted Answer

This statement is true. The length of one time period can be interpreted as any unit of time, such as one year, one month, one quarter, etc. depending on the context and needs of the calculation.

Question 10

The future value of $100 compounded semiannually for 3 years at 12% equals $140.49.
Calculation: $100 x1.4185 = $141.85.

Accepted Answer

To find the future value of $100 compounded semiannually for 3 years at 12%, we can use the formula:

FV = PV x (1 + r/n)^(nt)

Where PV is the present value, r is the annual interest rate, n is the number of times the interest is compounded in a year, t is the number of years.

In this case, we have:

PV = $100
r = 12% = 0.12
n = 2 (semiannually)
t = 3

So, FV = $100 x (1 + 0.12/2)^(2x3) = $141.85

Therefore, the statement "The future value of $100 compounded semiannually for 3 years at 12% equals $140.49" is false.

Question 11

An interest rate is also called a discount rate.

Accepted Answer

An interest rate is commonly referred to as a discount rate, particularly in relation to the valuation of future cash flows.

Question 12

Sandra has a savings account that has accumulated to $50,000. She started with $28,225, and earned interest at 10% compounded annually. It took her five years to accumulate the $50,000.
Calculation: $28,225/$50,000 = 0.5645. This is the present value of 1 factor, 10%, 6 periods.

Accepted Answer

The calculation provided is incorrect. The present value factor should be calculated using the formula for compound interest, not by dividing the initial amount by the final amount. Additionally, the correct number of periods should be 5, not 6.

Question 13

The future value of an ordinary annuity is the accumulated value of each annuity payment with interest one period after the date of the final payment.

Accepted Answer

The answer of The future value of an ordinary annuity...

Question 14

A company can use present and future value computations to estimate the interest component of holding assets over time.

Accepted Answer

Present and future value computations take into account the time value of money, which includes the interest component of holding assets over time. Therefore, a company can use these calculations to estimate the interest earned on assets held over a period of time.

Question 15

The present value of $5,000 per year for three years at 12% compounded annually is $12,009.
Calculation: $5,000 x 2.4018 = $12,009.

Accepted Answer

To calculate the present value of an annuity, we use the formula:

PV = A x [(1 - (1+r)^-n) / r]

where PV is the present value, A is the annual payment, r is the interest rate, and n is the number of periods.

In this case, we have A = $5,000, r = 12%, and n = 3. Plugging these values into the formula, we get:

PV = $5,000 x [(1 - (1+0.12)^-3) / 0.12] = $12,009.01 (rounded to the nearest cent)

Therefore, the statement is True.

Question 16

From the perspective of a depositor, a savings account is a liability with interest.

Accepted Answer

The answer of From the perspective of a depositor, a...

Question 17

The number of periods in a future value calculation can only be expressed in years.

Accepted Answer

The number of periods in a future value calculation can be expressed in any unit of time, such as months, quarters, or even days, depending on the frequency of compounding.

Question 18

With deposits of $5,000 at the end of each year, you will have accumulated $38,578 at the end of the sixth year if the annual rate of interest is 10%
Calculation: $5,000 x 7.7156 = $38,578.

Accepted Answer

The calculation is correct. Using the formula for future value of an annuity, which is FV = Pmt x (((1 + r)^n - 1) / r), where Pmt is the periodic payment (in this case, $5,000), r is the interest rate (10% or 0.1), and n is the number of periods (6 years or 6), we get:
FV = $5,000 x (((1 + 0.1)^6 - 1) / 0.1) = $38,578
Therefore, the statement is true.

Question 19

An annuity is a series of equal payments.

Accepted Answer

An annuity is a series of equal payments made at equal intervals, such as monthly or annually.

Question 20

At an annual interest rate of 8% compounded annually, $5,300 will accumulate to a total of $7,210.65 in 5 years.
Calculation: $7,210.65/$5,300 = 1.3605. This is the future value of 1 factor for 4 periods, 8%.

Accepted Answer

The calculation provided is incorrect. The future value of $5,300 at an 8% annual interest rate compounded annually for 5 years is calculated as $5,300 * (1 + 0.08)^5, which equals approximately $7,793.48, not $7,210.65.

Quiz 26: Time Value of Money

The present value of $2,000 to be received nine years from today at 8% interest compounded annually is $1,000. Calculation: $2,000 x 0.5002 = $1,000.