Question 1

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

Accepted Answer

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

Question 2

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 statement is true. The formula for future value is FV = P(1+i)^n, where FV is the future value, P is the present value, i is the interest rate, and n is the number of periods.

Question 3

Present and future value computations enable companies to measure or estimate the interest component of holding assets or liabilities over time.

Accepted Answer

Present and future value computations involve calculating the value of an asset or liability at a certain point in time, factoring in the interest earned or paid over time. This allows companies to make informed decisions about investments and financing options.

Question 4

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. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

Accepted Answer

Using the formula for future value of a single sum, $FV = PV(1 + r)^n$, where $PV = \$28,225$, $r = 10\% = 0.10$, and $n = 5$ years, we calculate $FV = \$28,225(1 + 0.10)^5 = \$28,225(1.61051) = \$45,488.77$, which is less than \$50,000.

Question 5

A series of equal payments made or received at the end of each period is an ordinary annuity.

Accepted Answer

This is the definition of an ordinary annuity.

Question 6

The present value of four $10,000 semiannual payments invested for 2 years at 12% compounded semiannually is $43,746. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

Accepted Answer

The present value of an annuity (PVA) can be calculated using the formula $PVA = PMT \times \left[\frac{1 - (1 + r)^{-n}}{r}\right]$, where PMT is the payment amount, r is the interest rate per period, and n is the total number of periods. Given a semiannual interest rate of 6% (12% annual rate divided by 2) and 4 total payments (2 years times 2 payments per year), the present value would not equal $43,746 when calculated correctly.

Question 7

Interest is the borrower's payment to the owner of an asset, for its use.

Accepted Answer

This is the definition of interest.

Question 8

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

Accepted Answer

From the perspective of an account holder, a savings account is an asset because it represents money that they have saved. The bank sees it as a liability because they owe the account holder the deposited funds plus any accrued interest.

Question 9

The present value of eight $5,000 semiannual payments invested for 4 years at 8% compounded semiannually is $33,663.50. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

Accepted Answer

This is a present value problem involving an annuity with semiannual payments and compounding. The formula to use is:

PV = Pmt * [1 - 1/(1+r)^n] / r   where r = periodic interest rate and n = number of periods

Given: Pmt = $5,000, n = 8 semiannual periods (4 years * 2), r = 8% / 2 = 4%

Using the formula, we have:

PV = $5,000 * [1 - 1/(1+0.04)^8] / 0.04
PV = $5,000 * [1 - 0.675564] / 0.04
PV = $33,663.50   (rounded to nearest cent)

This matches the given present value, so the answer is A)True.

Question 10

The present value of an annuity table can be used to determine the value today of a series of payments to be received in the future.

Accepted Answer

The present value of an annuity table is specifically designed to determine the value of a series of payments to be received in the future, discounted to their current value.

Question 11

The present value of $2,000 to be received nine years from today at 8% interest compounded annually is $1,000.40. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

Accepted Answer

This is true because the present value is calculated by dividing the future value by (1+i)^n, where i is the interest rate and n is the number of years. Using the present value factor from the tables provided, we can see that $1,000.40 is equal to $2,000/(1+0.08)^9.

Question 12

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. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

Accepted Answer

The present value factor of 0.7462 can be found using the formula PV = FV/(1+i)^n, where i is the interest rate per period and n is the number of periods. Plugging in the given values, we get PV = 6,300/(1+(0.10/2))^6 = 6,300/(1.05)^6 = 6,300*0.7462. Therefore, the statement is true.

Question 13

The future value of $100 compounded semiannually for 3 years at 12% equals $140.49. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

Accepted Answer

The future value of $100 compounded semiannually for 3 years at 12% is calculated using the formula $FV = PV \times (1 + r/n)^{nt}$, where $PV$ is the present value, $r$ is the annual interest rate, $n$ is the number of compounding periods per year, and $t$ is the time in years. Given $PV = $100$, $r = 12\% = 0.12$, $n = 2$, and $t = 3$, the calculation is $FV = $100 \times (1 + 0.12/2)^{2 \times 3}$, which does not equal $140.49. The correct calculation leads to a different amount.

Question 14

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 the worth of the asset at the future date.

Accepted Answer

The answer of The present value of 1 formula is...

Question 15

At an annual interest rate of 8% compounded annually, $5,300 will accumulate to a total of $7,210.65 in 5 years. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

Accepted Answer

To calculate the future value of $5,300 at an 8% annual interest rate compounded annually for 5 years, you use the formula $FV = PV \times (1 + r)^n$, where $PV$ is the present value, $r$ is the annual interest rate, and $n$ is the number of years. Using the given values, $FV = 5300 \times (1 + 0.08)^5$, which does not equal $7,210.65.

Question 16

An annuity is a series of equal payments occurring at equal intervals.

Accepted Answer

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

Question 17

An interest rate is also called a discount rate.

Accepted Answer

A discount rate is the interest rate used to determine the present value of future cash flows in a discounted cash flow analysis. Therefore, an interest rate is also called a discount rate.

Question 18

The present value of $5,000 per year for three years at 12% compounded annually is $12,009. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the tables provided.)

Accepted Answer

To calculate the present value of an annuity, we use the formula PV = C [(1 - 1/(1+r)^n)/r], where PV is the present value, C is the annuity payment, r is the interest rate, and n is the number of periods. Using this formula with the given values, we get PV = $5,000 [(1 - 1/(1+0.12)^3)/0.12] = $12,009. Therefore, the statement is true.

Question 19

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 is true. The time periods used in present value or future value tables can vary and can be interpreted as any length of time, whether it's one year, one month, or any other time frame.

Question 20

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

Accepted Answer

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

Quiz 14: Time Value of Money