Question 1

Assuming an interest rate of 10%, if you invest a lump sum of $4,000 now, the balance of your investment in 7 years will be closest to

Accepted Answer

The future value of a lump sum investment can be calculated using the formula FV = PV * (1 + r)^n, where PV is the present value ($4,000), r is the interest rate (10% or 0.10), and n is the number of years (7). Plugging in the values, FV = 4000 * (1 + 0.10)^7 = 4000 * 1.9487171 ≈ $7,796.

Question 2

Assuming an interest rate of 6%, the present value of $20,000 to be received 9 years from now would be closest to

Accepted Answer

Using the formula for present value of a future lump sum:

PV = FV / (1 + r)^n

where PV is the present value, FV is the future value, r is the interest rate, and n is the number of years.

Substituting the given values:

PV = 20,000 / (1 + 0.06)^9 
PV = 20,000 / 1.621
PV ≈ $12,345

Therefore, the closest option is A) $11,840.

Question 3

Assuming an interest rate of 10%, the present value of $40,000 to be received 8 years from now would be closest to

Accepted Answer

The answer of Assuming an interest rate of 10%, the...

Question 4

If you invest $1,000 at the end of every year for five years at an interest rate of 10%, the balance of your investment in 5 years will be closest to

Accepted Answer

Using the formula for the future value of an annuity:
FV = PMT x [(1 + r)^n - 1] / r
where:
PMT = payment (amount invested every year) = $1,000
r = interest rate = 10% = 0.1
n = number of periods = 5
FV = $1,610.51 x (1 + 0.1)^5 = $6,104.96
Therefore, the balance of the investment in 5 years will be closest to $6,105. Choice D is the correct answer.

Question 5

Calculating interest on the principal and on all the interest earned to date is called compound interest.

Accepted Answer

This statement accurately describes compound interest.

Question 6

Which term below is best described as the "relationship among principle, interest rate, and time"?

Accepted Answer

The relationship among principle, interest rate, and time is described as the time value of money. It involves calculating the present and future value of money based on the interest rate and time. Capital budgeting is the process of evaluating and selecting long-term investment opportunities, while payback period is a measure of how long it takes for an investment to pay back its initial cost. An annuity is a series of equal payments made at regular intervals. None of these terms capture the full relationship among principle, interest rate, and time.

Question 7

You win the lottery and must decide how to take the payout. Use an 8% discount rate. What is the present value of $10,000 a year received at the end of each of the next six years?

Accepted Answer

The present value of an annuity can be calculated using the formula PV = P * [(1 - (1 + r)^-n) / r], where P is the payment per period, r is the discount rate per period, and n is the number of periods. Plugging in the values ($10,000 for P, 0.08 for r, and 6 for n), the calculation gives a present value of approximately $46,230.

Question 8

Assuming an interest rate of 6%, the present value of $16,000 received at the end of each year for 6 years would be closest to

Accepted Answer

The present value of an annuity (a series of equal payments at regular intervals) can be calculated using the present value of annuity formula: $PV = P \times \left[\frac{1 - (1 + r)^{-n}}{r}\right]$, where $P$ is the payment amount, $r$ is the interest rate per period, and $n$ is the number of periods. Plugging in the values given: $P = $16,000$, $r = 0.06$, and $n = 6$, the calculation gives a present value of approximately $78,672, which is closest to option B.

Question 9

Your grandmother has promised to give you $2,000 a year at the end of each of the next four years if you earn Cs or better in all of your courses each year. Using a discount rate of 8%, which of the following is correct for determining the present value of the gift?

Accepted Answer

The present value of an annuity formula should be used to calculate the present value of the gift since it involves a series of payments (in this case, $2,000 per year) over a specific period of time (four years) at a given interest rate (8%). Therefore, the correct formula to use is PV = $2,000 × (Annuity PV factor, i = 8%, n = 4). Choice A is incorrect because it only calculates the interest earned, not the present value of the gift. Choice B uses an incorrect interest rate and does not account for the fact that there are multiple payments. Choice C is incorrect because it calculates the future value of the gift, not the present value.

Question 10

Assuming an interest rate of 10%, the present value of $12,000 received at the end of each year for 6 years would be closest to

Accepted Answer

The present value of an annuity can be calculated using the formula for the present value of an ordinary annuity. Using a 10% interest rate and 6 years, the present value is closest to $52,264.

Question 11

The principal amount and the interest rate are the only factors needed to calculate the time value of money.

Accepted Answer

The time period over which the interest is being earned or paid is also needed to calculate the time value of money. The formula typically used for this calculation is: FV = PV x (1 + r)n, where FV is the future value, PV is the present value, r is the interest rate, and n is the number of time periods.

Question 12

Assuming an interest rate of 6%, if you invest a lump sum of $6,000 now, the balance of your investment in 7 years will be closest to

Accepted Answer

The future value of a lump sum investment can be calculated using the formula FV = PV(1 + r)^n, where FV is the future value, PV is the present value (initial investment), r is the annual interest rate (expressed as a decimal), and n is the number of years. Plugging in the given values: FV = $6,000(1 + 0.06)^7 ≈ $9,024.

Question 13

Which of the following explains the time value of money?

Accepted Answer

The time value of money refers to the fact that invested money earns income over time, due to interest or other forms of investment return. This means that a dollar received today is worth more than a dollar received in the future, because the money received today can earn additional income if it is invested. Hence, option B is the correct answer. Options A, C, and D are not accurate descriptions of the time value of money.

Question 14

An ordinary annuity is is an annuity in which installments occur at the beginning of each period.

Accepted Answer

An ordinary annuity is an annuity in which installments occur at the end of each period.

Question 15

The Future Value of $1 table is used to calculate how much $100 would be worth in 5 years.

Accepted Answer

The Future Value of $1 table is used to calculate how much $1 would be worth in the future, given a certain interest rate and time period. It can be used to calculate the future value of any amount of money, not just $100.

Question 16

You won the lottery and have a number of choices as to how to take the money. Which choice yields a greater present value?

Accepted Answer

The answer of You won the lottery and have a...

Question 17

When computing the time value of money, the interest rate must always be expressed as an annual rate.

Accepted Answer

The interest rate can be expressed in different periods such as monthly, quarterly, or semi-annually, depending on the specifics of the calculation or agreement, and then adjusted to an annual rate if needed.

Question 18

Your rich aunt has promised to give you $3,000 a year at the end of each of the next four years to help with college. Using a discount rate of 10%, the present value of the gift can be stated as

Accepted Answer

To find the present value of an annuity, we use the annuity present value factor. In this case, the annuity present value factor with an interest rate of 10% and a term of 4 years is used. Therefore, the correct calculation for the present value of the gift would be:
PV = $3,000 x (1-1/(1+0.10)^4)/0.10 
PV = $9,703.07 (rounded to the nearest cent) 
Therefore, option C is the correct choice, as it uses the annuity present value factor.

Question 19

Which term below is best described as "a stream of equal periodic payments"?

Accepted Answer

An annuity is a stream of equal periodic payments, typically made either monthly or annually. It can be used for retirement savings, mortgages, or any situation where payments need to be made over a period of time. The other options, time value of money and capital budgeting, refer to broader financial concepts, while payback period specifically relates to the amount of time it takes for an investment to recoup its initial cost.

Question 20

The three factors that affect the time value of money are principal, number of periods, and interest rate.

Accepted Answer

The three factors that affect the time value of money are indeed principal, number of periods and interest rate.

Quiz 12: Capital Investment Decisions and the Time Value of Money