Question 1

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 2

When 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

When the discount rate is decreased, the discounting factor applied to calculate the present value of future cash flows decreases. This, in turn, increases the present value of any future cash flow. Therefore, choice B is the correct answer.

Question 3

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 discounting future cash payments back to the present using a discount factor. Option A is incorrect because present value involves converting future amounts into an initial amount. Option B is incorrect because the present value is not compounded, but rather discounted. Option D is incorrect because the future value of an investment is not the reciprocal of its present value, but rather the amount that an investment will be worth at a future point in time if it earns a certain rate of return.

Question 4

Leroy Diaz plans to invest some money today so that he will receive $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 5

Dat Nguyen is depositing $17,500 in an account paying an annual interest rate of 8.25 percent compounded monthly. What is the interest on interest after six years?
A) $8,662.50
B) $10,925.44
C) $2,497.63
D) $1,092.48

Accepted Answer

The interest on interest can be calculated using the formula for compound interest and then subtracting the simple interest (as if it were compounded annually) from it. The formula for compound interest is A = P(1 + r/n)^(nt), where A is the amount after t years, P is the principal amount ($17,500), r is the annual interest rate (0.0825), n is the number of times the interest is compounded per year (12), and t is the time the money is invested for (6 years). First, calculate the amount after 6 years using compound interest:A = 17500(1 + 0.0825/12)^(12*6) = 17500(1 + 0.006875)^(72) ≈ 17500 * 2.49763 ≈ $26,997.63Then, calculate the simple interest (as if it were compounded annually) for comparison:Simple interest = P(1 + rt) = 17500(1 + 0.0825*6) = 17500 * 1.495 = $26,162.50The interest on interest is the difference between these two amounts:$26,997.63 - $26,162.50 = $835.13However, the correct calculation involves finding the total compound interest and then subtracting the principal to find the total interest earned, and then calculating the interest on interest based on the difference between compound and simple interest over the period. The provided choices and explanation do not align with the correct calculation method, indicating a mistake in the calculation process. The correct approach to find the interest on interest involves more detailed steps to accurately calculate the difference between compound and simple interest over the specified period.

Question 6

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

To calculate the present value, we can use the formula: Present value = Future value / (1 + interest rate)^n, where n is the number of years. Plugging in the given values, we get: Present value = 25,000 / (1 + 0.075)^6 = $16,199 (rounded to the nearest dollar). Therefore, the best choice is C.

Question 7

When 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, the value of money decreases. Therefore, the present value of a future cash flow decreases.

Question 8

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

The answer of Tamera Watson is saving for her daughter's...

Question 9

Shawn Bowker invested $10,000 in a money market account that will pay 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 is the difference between the compound interest and the simple interest. First, calculate the compound interest using the formula A = P(1 + r/n)^(nt), where P is the principal, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the time in years. For daily compounding, n = 365. Then, calculate the simple interest using the formula SI = P * r * t. Subtract the simple interest from the compound interest to find the interest on interest.

Question 10

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 formula for calculating the future value of an investment when interest is compounded m times a year is FV = PV × (1 + i/m)^(m×n), where PV is the present value, i is the annual interest rate, m is the number of times the interest is compounded in a year, and n is the number of years. Option B is the closest match to this formula, with the substitution of S1S1P0S1U1P1nS1S1P0 for ^(m×n).

Question 11

Celesta Frank wants to go on a cruise in three years. She could earn 8.2 percent compounded monthly in an account if she were to deposit 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

The answer of Celesta Frank wants to go on a...

Question 12

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:

FV = PV(1 + r)^n

Where:
PV = present value (what Juan and Rachel need to deposit today)
r = annual interest rate (5.75%)
n = number of years (6)
FV = future value of the time-share ($16,860)

Substituting the given values, we have:

$16,860 = PV(1 + 0.0575)^6

Solving for PV:

PV = $12,055.29

Rounding off to the nearest dollar, the answer is $12,055. Therefore, the best choice is C.

Question 13

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 14

Jacob's friend, Albert, borrows 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 Jacob's friend, Albert, borrows today with a...

Question 15

Joseph Harris is considering an investment that pays 6.5 percent annually. How much must he invest today such 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

The answer of Joseph Harris is considering an investment that...

Question 16

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 correct equation to calculate the future value of an investment is FV_n = PV × (1 + i)ⁿ, where FV is the future value, PV is the present value, i is the interest rate, n is the number of periods, and t is the time. Choice A is incorrect because it divides PV by (1 + i)n instead of multiplying it. Choice C is incorrect because it adds (1 + i)n to PV instead of multiplying it. Choice D is incorrect because it divides (1 + i)n by PV instead of multiplying it.

Question 17

You need to have $15,000 in five years to payoff 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 18

The process of converting future cash flows to what its present value is called:
A) annualizing.
B) discounting.
C) compounding.
D) capital budgeting.

Accepted Answer

The process of converting future cash flows to their present value is known as discounting. Discounting is commonly used in financial analysis and valuation to determine the current worth of future cash flows. Approximately speaking, by calculating a present value of a sum of future cash you can determine how much money would be needed in the present to equal the future cash payments.

Question 19

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 20

Michael Peterson is seeking to accumulate $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

To find the present value, use the formula for compound interest: $ PV = \frac{FV}{(1 + r/n)^{nt}} $, where FV is the future value ($25,000), r is the annual interest rate (0.0635), n is the number of compounding periods per year (12), and t is the number of years (6). Calculating this gives approximately $17,097.

Quiz 5: The Time Value of Money

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

When discount rate:

Which of the following statements is true?

Leroy Diaz plans to invest some money today so that he will receive $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?

Dat Nguyen is depositing $17,500 in an account paying an annual interest rate of 8.25 percent compounded monthly. What is the interest on interest after six years?

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.)

When discount rate:

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

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

Celesta Frank wants to go on a cruise in three years. She could earn 8.2 percent compounded monthly in an account if she were to deposit 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.)

Jacob's friend, Albert, borrows 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.)

Joseph Harris is considering an investment that pays 6.5 percent annually. How much must he invest today such 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?

You need to have $15,000 in five years to payoff 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.)

The process of converting future cash flows to what its present value is called:

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.)

Michael Peterson is seeking to accumulate $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.)