Question 1

When the discount rate:
A) increases, the present value of a future cash flow decreases.
B) increases, the present value of a future cash flow increases.
C) decreases, the present value of a future cash flow will remain the same.
D) decreases, the present value of a future cash flow decreases.

Accepted Answer

When the discount rate increases, it means that the required rate of return on an investment is also increasing. This leads to a decrease in the present value of a future cash flow because the higher discount rate makes the future cash flow less valuable in today's dollars.

Question 2

Which of the following statements is true?
A) Present value calculations involve converting the initial amount into a future amount.
B) The present value (PV) is often called the compounded value of future cash payments.
C) The present value is calculated by using the discount factor.
D) The future value of an investment is the reciprocal of its present value.

Accepted Answer

The present value is calculated by using the discount factor, which is a percentage rate used to calculate the current worth of future cash payments. Option A is incorrect because PV calculations involve converting future amounts into their current (present) value. Option B is incorrect because the present value (PV) is the current value of future cash payments and is not compounded. Option D is incorrect because the future value is calculated by multiplying the present value with a factor that is dependent on the interest rate and the time period.

Question 3

Leroy Diaz plans to invest some money today so that he will have $7,500 in three years. If the investment he is considering will pay 3.65 percent compounded daily, how much will he have to invest today?
A) $5,276
B) $6,722
C) $6,897
D) $7,140

Accepted Answer

The answer of Leroy Diaz plans to invest some money...

Question 4

Celesta Frank wants to go on a cruise in three years. She could earn 8 percent compounded daily in an account if she deposits the money today. She needs to have $10,000 in three years. How much will she have to deposit today? (Round to the nearest dollar.)
A) $6,432
B) $7,826
C) $8,148
D) $7,763

Accepted Answer

To find the initial deposit, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where A is the final amount, P is the initial deposit, r is the interest rate (as a decimal), n is the number of times compounded per year, and t is the time in years.

In this case, we want to solve for P:

P = A/(1 + r/n)^(nt)

Plugging in the given values, we get:

P = 10000/(1 + 0.08/365)^(365*3)
P = $8,147.62

Rounding to the nearest dollar, the answer is $8,148, so the best choice is C.

Question 5

When the discount rate:
A) decreases, the present value of the future cash flow does not change.
B) decreases, the present value of any future cash flow increases.
C) increases, the present value of any future cash flow increases.
D) increases, the present value of any future cash flow does not change.

Accepted Answer

The discount rate is used to calculate the present value of future cash flows. When the discount rate decreases, the present value of any future cash flow will increase, because it is easier to turn future money into present money.

Question 6

Joseph Harris is considering an investment that pays 6.5 percent annually. How much does he need to invest today so that he will have $25,000 in seven years? (Round to the nearest dollar.)
A) $17,474
B) $18,850
C) $16,625
D) $16,088

Accepted Answer

To find the present value, use the formula: PV = FV / (1 + r)^n. Here, FV = $25,000, r = 0.065, and n = 7. Calculating gives PV = $25,000 / (1.065)^7 ≈ $16,088.

Question 7

Which of the following equations is used to calculate the future value of an investment when interest is compounded m times a year? A) FV_n = PV ÷ (1 + i)^m×n B) FV_n = PV × (1 + i/m)^m×n C) FV_n = (1 + i)^m×n+ PV D) FV_n = (1 + i)^m×n÷ PV

Accepted Answer

The correct formula for calculating the future value of an investment with compounded interest m times a year is FV = PV x (1 + i/m)^(m*n), where FV is the future value, PV is the present value, i is the interest rate, m is the number of times interest is compounded per year, and n is the number of years. This formula is equivalent to option B.

Question 8

Michael Peterson needs $25,000 in six years to invest in a real estate venture. He can earn 6.35 percent annual interest with monthly compounding in a private investment. How much will he have to invest today to reach his goal? (Round to the nearest dollar.)
A) $18,527
B) $23,015
C) $17,097
D) $19,648

Accepted Answer

The answer of Michael Peterson needs $25,000 in six years...

Question 9

Tamera Watson is saving for her daughter's college education. She wants to have $50,000 available when her daughter graduates from high school in four years. If the investment she is considering will pay 8.25 percent compounded monthly, how much will she have to invest today to reach her target? (Round to the nearest dollar.)
A) $35,987
B) $39,659
C) $41,275
D) $36,450

Accepted Answer

To find the present value, use the formula for compound interest: $ PV = \frac{FV}{(1 + r/n)^{nt}} $. Here, FV = $50,000, r = 0.0825, n = 12, t = 4. Plugging in these values gives approximately $35,987.

Question 10

Juan and Rachel Burpo plan to buy a time-share in six years of $16,860. In order to have adequate funds to do so, the Burpo want to make a deposit to their money market fund today. Assume that they will be able to earn an investment rate of 5.75%, compounded annually. How much will Juan and Rachel need to deposit today to achieve their goal? (Round off to the nearest dollar.)
A) $11,138
B) $8,885
C) $12,055
D) $14,243

Accepted Answer

We can use the formula for future value of a single sum with compound interest to determine the present value required:

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 = 16,860 / (1 + 0.0575)^6
PV = 12,055.41

Rounding off to the nearest dollar, the answer is $12,055, which corresponds to choice C.

Question 11

Evelyn has invested $10,000/year for ten years at an annual interest rate of 8%. Beginning in the 11th year interest rates decrease to 6%. Approximately how much does she have in her account after fifteen years (round to the nearest dollar)?
A) $27,590
B) $28,891
C) $31,722
D) $23,966

Accepted Answer

The future value of an annuity is given by the formula:FV = P * ((1 + r)^n - 1) / rwhere:P is the annual paymentr is the annual interest raten is the number of yearsIn this case, P = $10,000, r = 8% for the first 10 years and 6% for the next 5 years, and n = 15.For the first 10 years, the future value is:FV1 = $10,000 * ((1 + 0.08)^10 - 1) / 0.08 = $146,933For the next 5 years, the future value is:FV2 = $10,000 * ((1 + 0.06)^5 - 1) / 0.06 = $13,188The total future value is:FV = FV1 + FV2 = $146,933 + $13,188 = $160,121Rounding to the nearest dollar, the answer is $160,121.

Question 12

Which of the following equations is used to calculate the future value of an investment? A) FV_n = PV ÷ (1 + i)ⁿ B) FV_n = PV × (1 + i)ⁿ C) FV_n = (1 + i)ⁿ + PV D) FV_n = (1 + i)ⁿ ÷ PV

Accepted Answer

The equation for calculating the future value of an investment is FV = PV × (1 + i)^n, where FV is the future value of the investment, PV is the present value of the investment, i is the interest rate per compounding period, and n is the number of compounding periods. Option B is the only one that correctly represents this equation with the given variables.

Question 13

Celesta Frank wants to go on a cruise in three years. She could earn 8.2 percent compounded monthly in an account if she deposits the money today. She needs to have $10,000 in three years. How much will she have to deposit today? (Round to the nearest dollar.)
A) $6,432
B) $7,826
C) $8,148
D) $7,763

Accepted Answer

To find out how much Celesta needs to deposit today to have $10,000 in three years at an 8.2% annual interest rate compounded monthly, we use the formula for the present value of a single sum: $PV = \frac{FV}{(1 + r)^n}$, where $PV$ is the present value (amount she needs to deposit today), $FV$ is the future value ($10,000), $r$ is the monthly interest rate (annual rate divided by 12), and $n$ is the total number of compounding periods (months in 3 years).Given:- $FV = $10,000$- Annual interest rate = 8.2% or 0.082- Monthly interest rate $r = \frac{0.082}{12}$- Number of years = 3, so number of months $n = 3 \times 12 = 36$Plugging these values into the formula:$$PV = \frac{10,000}{(1 + \frac{0.082}{12})^{36}}$$$$PV = \frac{10,000}{(1 + 0.006833)^{36}}$$$$PV = \frac{10,000}{(1.006833)^{36}}$$$$PV = \frac{10,000}{1.276281}$$$$PV ≈ 7,826$$Therefore, Celesta needs to deposit approximately $7,826 today to have $10,000 in three years, given the conditions.

Question 14

Shawn Bowker invested $10,000 in a money market account that will pay an annual interest rate of 5.75 percent compounded daily. How much will the interest on interest be after two years?
A) $1,218.63
B) $1,150.00
C) $33.06
D) $68.63

Accepted Answer

The interest on interest, or compound interest, can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt) - P, where A is the amount of money accumulated after n years, including interest, P is the principal amount ($10,000), r is the annual interest rate (5.75% or 0.0575), n is the number of times that interest is compounded per year (daily, so 365), and t is the time the money is invested for in years (2 years). First, calculate the total amount after 2 years and then subtract the principal and the simple interest to find the interest on interest. Simple interest for 2 years would be P*r*t = $10,000*0.0575*2 = $1,150. Total compound interest can be calculated as follows: A = $10,000(1 + 0.0575/365)^(365*2) ≈ $11,218.63. Subtracting the principal and the simple interest from this gives the interest on interest: $11,218.63 - $10,000 - $1,150 = $68.63.

Question 15

Which of the following statements is true with respect to the present value of a future amount?
A) The higher the discount rate, the higher the present value of a single sum for a given time period.
B) The relation between present value and time is exponential.
C) The greater the time period, the higher the present value of a single sum for a given interest rate.
D) The lower the discount rate, the lower the present value of a single sum for a given time period.

Accepted Answer

The relation between present value and time is exponential because the present value is calculated using the formula PV = FV / (1 + r)^n, where PV is the present value, FV is the future value, r is the discount rate, and n is the number of periods. This formula shows an exponential relationship between the present value and time.

Question 16

Robert Kelly wants to start a business in 10 years. He hopes to have $100,000 at that time to invest in the business. To reach his goal, he plans to invest a certain amount today in a bank CD that will pay him 9.50 percent annually. How much will he have to invest today to achieve his target? (Round to the nearest dollar.)
A) $54,233
B) $63,837
C) $91,324
D) $40,351

Accepted Answer

To find out how much Robert Kelly needs to invest today to achieve his target of $100,000 in 10 years at an annual interest rate of 9.50%, we use the formula for the present value of a single sum, which is: Present Value = Future Value / (1 + r)^n, where r is the annual interest rate (as a decimal) and n is the number of years. Plugging in the values: Present Value = $100,000 / (1 + 0.095)^10 = $100,000 / (1.095)^10 ≈ $40,351 (rounded to the nearest dollar).

Question 17

Steve Fisher is saving for a new car. He needs to have $ 21,000 for the car in three years. How much will he have to invest today in an account paying 8 percent annually to achieve his target? (Round to nearest dollar.)
A) $22,680
B) $26,454
C) $16,670
D) $19,444

Accepted Answer

To find out how much Steve needs to invest today to reach his goal of $21,000 in three years at an 8% annual interest rate, we use the formula for the present value of a single sum: PV = FV / (1 + r)^n, where PV is the present value (amount to invest today), FV is the future value ($21,000), r is the annual interest rate (8% or 0.08), and n is the number of years (3). Plugging in the values, we get PV = $21,000 / (1 + 0.08)^3, which calculates to approximately $16,670 when rounded to the nearest dollar.

Question 18

Joyce Thomas wants to buy a house in six years. She hopes to have $25,000 at that time. If the bank CD she wants to invest in will pay 7.5 percent annually, how much will she have to invest today? (Round to the nearest dollar.)
A) $18,472
B) $13,987
C) $16,199
D) $23,256

Accepted Answer

We can use the formula for future value of a single sum with compound interest:

FV = PV x (1 + r)n

Where: 
PV = present value (amount to be invested today)
r = annual interest rate
n = number of periods (in this case, 6 years)

We want to solve for PV, so we can rearrange the formula:

PV = FV / (1 + r)n

Plugging in the values:

PV = 25,000 / (1 + 0.075)6
PV = 16,198.54

Rounding to the nearest dollar, the answer is C) $16,199.

Question 19

You need to have $15,000 in five years to pay off a home equity loan. You can invest in an account that pays 5.75 percent compounded quarterly. How much will you have to invest today to attain your target in five years? (Round to the nearest dollar.)
A) $4,903
B) $11,275
C) $13,184
D) $12,250

Accepted Answer

To find out how much you need to invest today to reach a future sum with an account that compounds interest quarterly, you can use the formula for the present value of a future sum: $PV = \frac{FV}{(1 + r)^n}$, where PV is the present value (amount you need to invest today), FV is the future value ($15,000), r is the quarterly interest rate (annual rate divided by 4), and n is the total number of compounding periods (years times 4, since it compounds quarterly). Given an annual interest rate of 5.75%, the quarterly rate is $0.0575 / 4 = 0.014375$, and with 5 years of compounding quarterly, $n = 5 \times 4 = 20$. Plugging these values into the formula gives $PV = \frac{15,000}{(1 + 0.014375)^{20}}$, which when calculated and rounded to the nearest dollar, gives approximately $11,275.

Question 20

Albert borrows money from Jacob today with a promise to repay $7,418.87 in four years. If Jacob could earn 5.45 percent annually on the any investment he makes today, how much would he be willing to lend Albert today? (Round to nearest dollar.)
A) $6,000
B) $7,035
C) $6,500
D) $7,150

Accepted Answer

The answer of Albert borrows money from Jacob today with...

Quiz 5: The Time Value of Money

When the discount rate:

Which of the following statements is true?

Leroy Diaz plans to invest some money today so that he will have $7,500 in three years. If the investment he is considering will pay 3.65 percent compounded daily, how much will he have to invest today?

Celesta Frank wants to go on a cruise in three years. She could earn 8 percent compounded daily in an account if she deposits the money today. She needs to have $10,000 in three years. How much will she have to deposit today? (Round to the nearest dollar.)

When the discount rate:

Joseph Harris is considering an investment that pays 6.5 percent annually. How much does he need to invest today so that he will have $25,000 in seven years? (Round to the nearest dollar.)

Which of the following equations is used to calculate the future value of an investment when interest is compounded m times a year?

Michael Peterson needs $25,000 in six years to invest in a real estate venture. He can earn 6.35 percent annual interest with monthly compounding in a private investment. How much will he have to invest today to reach his goal? (Round to the nearest dollar.)

Evelyn has invested $10,000/year for ten years at an annual interest rate of 8%. Beginning in the 11th year interest rates decrease to 6%. Approximately how much does she have in her account after fifteen years (round to the nearest dollar) ?

Which of the following equations is used to calculate the future value of an investment?

Celesta Frank wants to go on a cruise in three years. She could earn 8.2 percent compounded monthly in an account if she deposits the money today. She needs to have $10,000 in three years. How much will she have to deposit today? (Round to the nearest dollar.)

Shawn Bowker invested $10,000 in a money market account that will pay an annual interest rate of 5.75 percent compounded daily. How much will the interest on interest be after two years?

Which of the following statements is true with respect to the present value of a future amount?

Steve Fisher is saving for a new car. He needs to have $ 21,000 for the car in three years. How much will he have to invest today in an account paying 8 percent annually to achieve his target? (Round to nearest dollar.)

Joyce Thomas wants to buy a house in six years. She hopes to have $25,000 at that time. If the bank CD she wants to invest in will pay 7.5 percent annually, how much will she have to invest today? (Round to the nearest dollar.)

You need to have $15,000 in five years to pay off a home equity loan. You can invest in an account that pays 5.75 percent compounded quarterly. How much will you have to invest today to attain your target in five years? (Round to the nearest dollar.)

Albert borrows money from Jacob today with a promise to repay $7,418.87 in four years. If Jacob could earn 5.45 percent annually on the any investment he makes today, how much would he be willing to lend Albert today? (Round to nearest dollar.)