Podcast
Questions and Answers
What is the maximum total fee a borrower would accumulate when rolling over an initial $100 payday loan four times over a 10-week period?
What is the maximum total fee a borrower would accumulate when rolling over an initial $100 payday loan four times over a 10-week period?
- $50
- $75 (correct)
- $150
- $100
What is the annualized nominal rate derived from a 2-week payday loan rate of 15%?
What is the annualized nominal rate derived from a 2-week payday loan rate of 15%?
- 195%
- 420%
- 750%
- 391% (correct)
What is the necessary annual cash payment to accumulate a future value of $30,000 in 5 years at an annual interest rate of 6%?
What is the necessary annual cash payment to accumulate a future value of $30,000 in 5 years at an annual interest rate of 6%?
- $5,000 (correct)
- $6,000
- $4,500
- $6,500
What is the primary purpose of a loan amortization schedule?
What is the primary purpose of a loan amortization schedule?
What is the present value of $1,700 to be received in 8 years with an opportunity cost of 8%?
What is the present value of $1,700 to be received in 8 years with an opportunity cost of 8%?
If a loan of $6,000 is borrowed at 10% over 4 years, what is the componenet that must be calculated to determine the size of payments?
If a loan of $6,000 is borrowed at 10% over 4 years, what is the componenet that must be calculated to determine the size of payments?
How does rolling over a payday loan affect total fees paid by the borrower?
How does rolling over a payday loan affect total fees paid by the borrower?
In what manner does an annuity due differ from an ordinary annuity?
In what manner does an annuity due differ from an ordinary annuity?
What does loan amortization primarily involve?
What does loan amortization primarily involve?
What impact does compounding interest for an additional period have on an annuity due compared to an ordinary annuity?
What impact does compounding interest for an additional period have on an annuity due compared to an ordinary annuity?
Which equation can be used to find the future value of an ordinary annuity?
Which equation can be used to find the future value of an ordinary annuity?
Which factor is important when calculating the effective annual interest rate for a payday loan?
Which factor is important when calculating the effective annual interest rate for a payday loan?
If Fran Abrams chooses an ordinary annuity earning 7% annually, what will be the method to calculate her future savings?
If Fran Abrams chooses an ordinary annuity earning 7% annually, what will be the method to calculate her future savings?
How are cash flows defined in the context of annuities?
How are cash flows defined in the context of annuities?
Which statement accurately reflects the nature of annuities?
Which statement accurately reflects the nature of annuities?
What is the total cash flow for both annuity A and annuity B in Fran Abrams' example?
What is the total cash flow for both annuity A and annuity B in Fran Abrams' example?
What does the variable FVn represent in the future value equation?
What does the variable FVn represent in the future value equation?
If Jane Farber invests $800 at an interest rate of 6%, what will be the future value after 5 years?
If Jane Farber invests $800 at an interest rate of 6%, what will be the future value after 5 years?
What is the primary principle behind present value?
What is the primary principle behind present value?
In the calculation of present value, what role does the discount rate play?
In the calculation of present value, what role does the discount rate play?
How is present value (PV) calculated using the future value (FVn)?
How is present value (PV) calculated using the future value (FVn)?
What can be inferred if an amount invested today earns no interest over time?
What can be inferred if an amount invested today earns no interest over time?
Which of the following describes the process of discounting cash flows?
Which of the following describes the process of discounting cash flows?
If Paul Shorter can earn an interest rate of 6%, what is the maximum he should pay now for a future amount of $300?
If Paul Shorter can earn an interest rate of 6%, what is the maximum he should pay now for a future amount of $300?
What is the main advantage of compounding interest more frequently than annually?
What is the main advantage of compounding interest more frequently than annually?
If Frey Company expects an investment return of at least 9%, what should it consider when determining how much to pay for the cash flow opportunity?
If Frey Company expects an investment return of at least 9%, what should it consider when determining how much to pay for the cash flow opportunity?
How does earning interest on interest impact the effective interest rate?
How does earning interest on interest impact the effective interest rate?
What is considered a mixed stream of cash flows?
What is considered a mixed stream of cash flows?
What would be the effect of a higher discount rate on the present value of future cash flows?
What would be the effect of a higher discount rate on the present value of future cash flows?
When is the best time to invest cash flows to maximize future value?
When is the best time to invest cash flows to maximize future value?
What is the relationship between nominal interest rate and effective interest rate when compounding occurs more frequently than annually?
What is the relationship between nominal interest rate and effective interest rate when compounding occurs more frequently than annually?
If Shrell Industries receives cash flows over 5 years and invests them immediately at 8%, what method can be used to determine how much they will accumulate?
If Shrell Industries receives cash flows over 5 years and invests them immediately at 8%, what method can be used to determine how much they will accumulate?
What happens to a borrower with an adjustable-rate mortgage (ARM) when home prices begin to decline?
What happens to a borrower with an adjustable-rate mortgage (ARM) when home prices begin to decline?
What is the formula used to calculate the compound annual rate of return?
What is the formula used to calculate the compound annual rate of return?
How much is Ray Noble's investment worth after four years if it was initially purchased for $1,250?
How much is Ray Noble's investment worth after four years if it was initially purchased for $1,250?
If Jan Jacobs borrows $2,000 and pays back $514.14 annually for 5 years, what method is being used to repay the loan?
If Jan Jacobs borrows $2,000 and pays back $514.14 annually for 5 years, what method is being used to repay the loan?
How much equity can help a homeowner reduce their mortgage payment?
How much equity can help a homeowner reduce their mortgage payment?
What percentage rate did Ray earn annually on his investment worth $1,520 after 4 years from an initial amount of $1,250?
What percentage rate did Ray earn annually on his investment worth $1,520 after 4 years from an initial amount of $1,250?
What occurred in 2006 that significantly impacted subprime mortgage borrowers?
What occurred in 2006 that significantly impacted subprime mortgage borrowers?
Which factor contributed to lenders tightening lending standards after 2006?
Which factor contributed to lenders tightening lending standards after 2006?
What is the method used to find the periodic deposit required to accumulate a given future sum?
What is the method used to find the periodic deposit required to accumulate a given future sum?
Which method is appropriate for amortizing a loan into equal periodic payments?
Which method is appropriate for amortizing a loan into equal periodic payments?
How can interest or growth rates be determined in financial calculations?
How can interest or growth rates be determined in financial calculations?
Which equation is used to estimate an unknown number of periods in a financial scenario?
Which equation is used to estimate an unknown number of periods in a financial scenario?
In loan amortization, which aspect is crucial to determine?
In loan amortization, which aspect is crucial to determine?
What is typically not considered when estimating an unknown interest rate in financial calculations?
What is typically not considered when estimating an unknown interest rate in financial calculations?
What does the procedure of finding the future value of an annuity primarily assist with?
What does the procedure of finding the future value of an annuity primarily assist with?
Which of these statements accurately describes loan amortization?
Which of these statements accurately describes loan amortization?
Flashcards
Future Value (FV)
Future Value (FV)
The amount an investment will grow to after n periods at a specific interest rate.
Present Value (PV)
Present Value (PV)
Current worth of a future sum of money, discounted back at a specific interest rate.
FV Formula
FV Formula
FVn = PV × (1 + r)ⁿ, where r is the interest rate and n is the number of periods.
Compounded Interest
Compounded Interest
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Discount Rate
Discount Rate
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PV Formula
PV Formula
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Investment Growth
Investment Growth
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Investment Opportunity
Investment Opportunity
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Future Value of a Mixed Stream
Future Value of a Mixed Stream
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Present Value of a Mixed Stream
Present Value of a Mixed Stream
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Compounding Interest
Compounding Interest
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Effective Interest Rate
Effective Interest Rate
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Nominal Interest Rate
Nominal Interest Rate
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Investment Return
Investment Return
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Cash Flow Stream
Cash Flow Stream
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Discounting Future Cash Flows
Discounting Future Cash Flows
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Loan Amortization Schedule
Loan Amortization Schedule
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Subprime Mortgages
Subprime Mortgages
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Adjustable-Rate Mortgages (ARMs)
Adjustable-Rate Mortgages (ARMs)
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Equity in Home
Equity in Home
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Compound Annual Growth Rate (CAGR)
Compound Annual Growth Rate (CAGR)
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Investment Value Calculation
Investment Value Calculation
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Annual Payment Amount
Annual Payment Amount
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Finding Interest Rate on Loans
Finding Interest Rate on Loans
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Payday Loan
Payday Loan
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Annualized Fee Rate
Annualized Fee Rate
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Loan Amortization
Loan Amortization
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Amortization Schedule
Amortization Schedule
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Periodic Payments (CF)
Periodic Payments (CF)
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Periodic Deposit Calculation
Periodic Deposit Calculation
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Estimating Interest Rates
Estimating Interest Rates
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Calculating Unknown Periods
Calculating Unknown Periods
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Future Value of Annuity
Future Value of Annuity
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Present Value of Annuity
Present Value of Annuity
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Interest Rate Calculation
Interest Rate Calculation
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Count of Periods
Count of Periods
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Ordinary Annuity
Ordinary Annuity
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Annuity Due
Annuity Due
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Interest Compounding
Interest Compounding
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Cash Flow
Cash Flow
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Future Value of an Annuity
Future Value of an Annuity
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Opportunity Cost
Opportunity Cost
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Study Notes
Chapter 5: Time Value of Money
- This chapter covers the fundamental concepts of time value in finance, including the use of computational tools and the basic patterns of cash flow.
- Learning Goals (LG1-LG6): LG1 discusses the role of time value, computational tools, and cash flow patterns. LG2 explains future value and present value calculations for single amounts and their relationship. LG3 calculates future and present values of ordinary annuities and annuities due, and the present value of a perpetuity. LG4 calculates the future and present value of a mixed cash flow stream. LG5 explores the effect of compounding interest more frequently than annually on future value and the effective annual interest rate. LG6 describes methods for determining deposits needed to accumulate a future sum, loan amortization, finding interest or growth rates, and calculating unknown periods.
- Future Value vs. Present Value: The text introduces the concept of valuing future cash flows in today's dollars (present value) versus today's money in future terms (future value). A timeline example of a company's cash flow is given.
- Computational Tools: Financial calculators and spreadsheets offer built-in time value functions. Calculator keys and spreadsheet functions are described. Cash flows are represented as either positive (inflows) or negative (outflows).
- Cash Flow Patterns: Three key patterns—single amount, annuities (level periodic cash flows), and mixed cash flows are examined.
- Future Value of a Single Amount: Defined as the value at a future date of a sum invested today, earning interest over a specific period. The concept of compound interest is explored. Principal is the base amount on which interest is calculated, while a detailed example of Fred Moreno's account is provided. A general equation for the future value of a single amount is also presented for understanding.
- Present Value of a Single Amount: The current value of a future amount; the amount required today to generate a given future value at a predetermined rate of interest. A personal finance example of calculating this is given; also, a personal finance example showing how computer programming and calculator keys and functions can be used to find present values is provided. A general formula is also shown.
- Annuities: This section details ordinary annuities (payments at the end of each period) and annuity due (payments at the beginning). Examples, calculations, and the differences between ordinary and annuity due payments are discussed.
- Finding the Future Value of an Ordinary Annuity: A formula is given to calculate the future value of an ordinary annuity, including an example. The formula for calculating the future value of an ordinary annuity is presented. Examples of problems are given to show how to calculate the future value of an annuity.
- Finding the Present Value of an Ordinary Annuity: The formula to calculate the present value of an ordinary annuity is provided, along with examples.
- Finding the Future Value of an Annuity Due: A formula to calculate the future value of an annuity due is presented and examples are given.
- Finding the Present Value of an Annuity Due: The formula for calculating the present value of an annuity due is included, along with examples.
- Perpetuities: defined as an annuity with an infinite life. The formula to calculate the present value of a perpetuity is presented. Example problems are provided to illustrate their use.
- Future Value of a Mixed Stream: A method for calculating the future value of a mixed cash flow stream is demonstrated.
- Finding the Present Value of a Mixed Stream: A method for calculating the present value of a mixed cash flow stream.
- Compounding Interest More Frequently Than Annually: This section explains the effective annual rate (EAR) and how it differs from the stated/nominal annual rate. Specific examples, including semiannual and quarterly compounding, are given.
- Continuous Compounding: The continuous compounding formula is presented, along with an example problem.
- Nominal and Effective Annual Rates of Interest: Definitions and the formula for calculating the effective annual rate are provided.
- Special Applications: Deposits Needed to Accumulate a Future Sum, Loan Amortization, Finding Interest or Growth Rates, Finding an Unknown Number of Periods: Formulas and examples for each are described.
- Chapter Resources: MyFinanceLab with chapter cases, group exercises, and critical thinking problems.
- Integrative Case: Track Software, Inc. (Tables 1-5, and related questions): The financial statements for Track Software are presented, and the corresponding analysis and practical applications of financial goals are emphasized. A case study.
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