Question 1

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 can be used to calculate the present value of the gift, because the grandmother is promising to give $2,000 at the end of each year in the next four years. The formula is PV = PMT x [(1 - (1/(1+i)^n))/i], where PMT is the annual payment, i is the interest rate, and n is the number of years. Using a discount rate of 8%, the present value of the gift is calculated as PV = $2,000 x [(1 - (1/(1+0.08)^4))/0.08] = $6,634.16. Therefore, choice D is the correct answer.

Question 2

Which of the following affects the present value of an investment?

Accepted Answer

All of the factors listed (interest rate, number of time periods, and type of investment) can affect the present value of an investment. The interest rate directly affects the amount of future cash flows that are being discounted to present value. The longer the investment horizon (number of time periods), the greater the impact of compounding, which can increase the present value of an investment. The type of investment (annuity versus lump sum) can also affect the present value calculation since an annuity provides a regular stream of cash flows, while a lump sum provides a one-time payment.

Question 3

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 the future value of any amount, not just $1. It shows how much a certain amount invested today will be worth in the future, based on a certain interest rate and time period. So, it can also be used to calculate how much $100 would be worth in 5 years.

Question 4

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

Accepted Answer

The time period (number of years, months or days) over which the interest is compounded or discounted is also required to calculate the time value of money.

Question 5

If you invest $4,000 at the end of every year for nine years at an interest rate of 6%,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 * ((1 + r)^n - 1) / r
where Pmt is the payment made at the end of each year, r is the interest rate, and n is the number of years.

In this case, Pmt = $4,000, r = 6%, and n = 9.

The balance of the investment in 5 years would be the future value of the annuity for the first 5 years, plus the future value of the individual $4,000 payment made at the end of the 5th year.

Future value of the annuity for 5 years:
FV = $4,000 * ((1 + 0.06)^5 - 1) / 0.06 = $25,496.76

Future value of the single $4,000 payment after 5 years:
FV = $4,000 * (1 + 0.06)^5 = $5,352.03

Total balance of the investment after 5 years:
$25,496.76 + $5,352.03 = $30,848.79

Therefore, the closest option is $22,548.

Question 6

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 future value of an annuity:
FV = PMT x ((1+r)^n - 1) / r 
where PMT is the annual payment, r is the interest rate, and n is the number of years

In this case: 
PMT = $1,000
r = 10%
n = 5

FV = $1,000 x ((1+0.10)^5 - 1) / 0.10
FV = $1,000 x (1.6105 - 1) / 0.10
FV = $1,000 x 6.105
FV = $6,105

Therefore, the balance of your investment in 5 years will be closest to $6,105, which is answer choice D.

Question 7

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

We can use the formula for present value of an annuity:

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

where PV is the present value, PMT is the amount received at the end of each year, r is the interest rate per period (in this case, per year), and n is the number of periods (in this case, 6 years).

Plugging in the values we have:

PV = $12,000 x [(1 - (1+0.1)^-6)/0.1]
PV = $12,000 x [(1 - 0.564474)/0.1]
PV = $12,000 x [9.592677]
PV = $115,112.11

Therefore, the present value of $12,000 received at the end of each year for 6 years at an interest rate of 10% is approximately $52,260.

Question 8

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...

Question 9

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 10

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

Accepted Answer

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

Question 11

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 compounding periods, such as monthly or quarterly, depending on the context of the financial calculation.

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 PV is the present value ($6,000), r is the interest rate (0.06), and n is the number of years (7). Calculating this gives FV = 6000 * (1 + 0.06)^7 ≈ $9,024.

Question 13

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 can be calculated using the formula: PV = PMT × [(1 - (1 + r)^-n) / r], where PMT is the annual payment, r is the interest rate, and n is the number of periods. Plugging in the values: PV = $16,000 × [(1 - (1 + 0.06)^-6) / 0.06] ≈ $78,672.

Question 14

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 is the sum of the present values of each of the individual payments. The present value of each payment is calculated by dividing the payment by (1 + r)^n, where r is the discount rate and n is the number of years from now that the payment will be received. In this case, the discount rate is 8% and the payments will be received at the end of each of the next six years. So, the present value of each payment is:PV = $10,000 / (1 + 0.08)^nThe present value of the annuity is the sum of the present values of each of the individual payments:PV = $10,000 / (1 + 0.08)^1 + $10,000 / (1 + 0.08)^2 + $10,000 / (1 + 0.08)^3 + $10,000 / (1 + 0.08)^4 + $10,000 / (1 + 0.08)^5 + $10,000 / (1 + 0.08)^6PV = $46,230

Question 15

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 16

The net present value method incorporates the time value of money.

Accepted Answer

The net present value method takes into account the time value of money by discounting future cash flows to their present value. This allows for a fair comparison of investment options, even if the cash flows occur at different points in time.

Question 17

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

The present value of an annuity formula is used to calculate the present value of a series of equal payments received or paid out over a specified time period in the future. In this case, the gift of $3,000 is an annuity that will be received at the end of each of the next four years. Using the annuity present value factor with a discount rate of 10% and a time period of four years, we can calculate the present value of the gift as PV = $3,000 x 3.1699 = $9,509.70. Therefore, the best choice is C.

Question 18

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

We can use the Present Value formula to solve the problem:

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, we get:

PV = 20,000 / (1 + 0.06)^9
PV = 20,000 / 1.63
PV = 12,270.90

The closest option to this value is A) $11,840. Therefore, the answer is A.

Question 19

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

Accepted Answer

This statement accurately defines compound interest.

Question 20

Which of the following explains the time value of money?

Accepted Answer

The time value of money concept states that money available now is worth more than the same amount in the future due to its potential earning capacity, which is primarily due to the ability to earn income or interest over time.

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