Podcast
Questions and Answers
If you have $15,000 and need $20,000 for a car, and your investment yields 10% annually, approximately how many years will it take to reach your goal?
If you have $15,000 and need $20,000 for a car, and your investment yields 10% annually, approximately how many years will it take to reach your goal?
- 3.5 years
- 2.5 years
- 3.0 years (correct)
- 4.0 years
If you want to buy a house for $150,000 and need a 10% down payment plus 5% of the loan amount for closing costs, how much money do you need in total?
If you want to buy a house for $150,000 and need a 10% down payment plus 5% of the loan amount for closing costs, how much money do you need in total?
- $22,500
- $16,750
- $15,000
- $21,750 (correct)
With a $15,000 initial investment and a 7.5% annual return, about how many years will it take to reach the required $21,750 for the down payment and closing costs of a house?
With a $15,000 initial investment and a 7.5% annual return, about how many years will it take to reach the required $21,750 for the down payment and closing costs of a house?
- 5.5 years
- 4.0 years
- 4.5 years
- 5.1 years (correct)
What is the key characteristic of an ordinary annuity?
What is the key characteristic of an ordinary annuity?
Which of the following is an example of an annuity due?
Which of the following is an example of an annuity due?
What defines a perpetuity in finance?
What defines a perpetuity in finance?
How do you calculate the present or future value of an annuity due after computing it as if it were an ordinary annuity?
How do you calculate the present or future value of an annuity due after computing it as if it were an ordinary annuity?
What does the process of discounting primarily determine?
What does the process of discounting primarily determine?
What is the formula to find the present value of a perpetuity where the payment is PMT and the discount rate is r?
What is the formula to find the present value of a perpetuity where the payment is PMT and the discount rate is r?
If you want to find the present value of $1000 received in 2 years time with an interest rate of 5%, what is the correct calculation?
If you want to find the present value of $1000 received in 2 years time with an interest rate of 5%, what is the correct calculation?
Assuming the same interest rate, which is true about the relationship between time period and present value?
Assuming the same interest rate, which is true about the relationship between time period and present value?
What tends to happen to the present value of a future sum, as the interest rate increases?
What tends to happen to the present value of a future sum, as the interest rate increases?
If a future value is $2000 and the present value is $1000, and the interest rate was 10%, what is the number of periods(t)?
If a future value is $2000 and the present value is $1000, and the interest rate was 10%, what is the number of periods(t)?
What is the 'discounting factor' used for when finding the present value of a future sum?
What is the 'discounting factor' used for when finding the present value of a future sum?
Which of the following Excel functions can be used to compute present value?
Which of the following Excel functions can be used to compute present value?
If you need $10,000 in 2 years and can earn 5% annually, what is the present value you need today?
If you need $10,000 in 2 years and can earn 5% annually, what is the present value you need today?
If you deposit $1500,$1000 and $500 at the end of each year for the next 3 years, earning a 6% interest rate, what is the present value of these cash flows?
If you deposit $1500,$1000 and $500 at the end of each year for the next 3 years, earning a 6% interest rate, what is the present value of these cash flows?
Using the same cash flows ($1500, $1000 and $500) and interest rate (6%), what is the future value of these investments at the end of 3 years?
Using the same cash flows ($1500, $1000 and $500) and interest rate (6%), what is the future value of these investments at the end of 3 years?
What is the combined present value of receiving $1,000 in 7 years and $1,000 in 10 years, assuming a discount rate of 6%?
What is the combined present value of receiving $1,000 in 7 years and $1,000 in 10 years, assuming a discount rate of 6%?
Which of the following best describes the Annual Percentage Rate (APR)?
Which of the following best describes the Annual Percentage Rate (APR)?
How do you calculate the per-period interest rate from the APR?
How do you calculate the per-period interest rate from the APR?
If you have a credit card with a 1.5% monthly interest rate and a $1,000 balance, approximately how many years will it take to pay off the balance assuming no additional charges?
If you have a credit card with a 1.5% monthly interest rate and a $1,000 balance, approximately how many years will it take to pay off the balance assuming no additional charges?
A loan of $2,000 is taken at a 5% annual interest rate, with annual payments of $734.42. How many years will it take to pay off this loan?
A loan of $2,000 is taken at a 5% annual interest rate, with annual payments of $734.42. How many years will it take to pay off this loan?
You borrow $10,000 from your parents to purchase a car, agreeing to pay $207.58 per month for 60 months. What is the monthly interest rate on this loan?
You borrow $10,000 from your parents to purchase a car, agreeing to pay $207.58 per month for 60 months. What is the monthly interest rate on this loan?
Your firm is purchasing a $100,000 warehouse, with the bank requiring a 20% down payment. If the bank offers a 30 year-loan with equal annual payments, what will be the loan amount?
Your firm is purchasing a $100,000 warehouse, with the bank requiring a 20% down payment. If the bank offers a 30 year-loan with equal annual payments, what will be the loan amount?
For the warehouse purchase described, if it is a 30-year loan at an 8% annual interest rate, what additional information would be needed to determine the annual loan payment?
For the warehouse purchase described, if it is a 30-year loan at an 8% annual interest rate, what additional information would be needed to determine the annual loan payment?
If you know the loan amount, the number of monthly payments and the monthly payment amount, which of these can you calculate?
If you know the loan amount, the number of monthly payments and the monthly payment amount, which of these can you calculate?
If you know all other parameters, how does increasing the number of payments affect the annual payment amount while keeping the principle constant?
If you know all other parameters, how does increasing the number of payments affect the annual payment amount while keeping the principle constant?
Which function in excel is used to calculate number of periods required to pay off a loan when all other variables are known?
Which function in excel is used to calculate number of periods required to pay off a loan when all other variables are known?
If the account earns 12% per year, how much will Ellen have saved at age 6, assuming she invested $10,000?
If the account earns 12% per year, how much will Ellen have saved at age 6, assuming she invested $10,000?
In the Future value of Annuity calculation, what does the variable 'i' represent?
In the Future value of Annuity calculation, what does the variable 'i' represent?
In the formula for the future value of an annuity, the variable $n$ usually refers to:
In the formula for the future value of an annuity, the variable $n$ usually refers to:
What is the future value of an annuity used to calculate?
What is the future value of an annuity used to calculate?
What does the variable 'P' stand for in the future value of an ordinary annuity formula?
What does the variable 'P' stand for in the future value of an ordinary annuity formula?
Using the formula given, if Ellen deposits $20,000 into an account with 7% interest per year, after how many years will she have approximately $6,645 interest earned?
Using the formula given, if Ellen deposits $20,000 into an account with 7% interest per year, after how many years will she have approximately $6,645 interest earned?
What is the key difference between calculating the future value of a single sum versus the future value of an annuity?
What is the key difference between calculating the future value of a single sum versus the future value of an annuity?
If an investment has a negative interest rate, how will this appear in the standard future value of an annuity formula?
If an investment has a negative interest rate, how will this appear in the standard future value of an annuity formula?
If Ellen makes 3 deposits of $10,000, how many times would the interest earned be compounded in the future value of annuity calculation?
If Ellen makes 3 deposits of $10,000, how many times would the interest earned be compounded in the future value of annuity calculation?
How many deposits are needed to calculate the 'future value of annuity'?
How many deposits are needed to calculate the 'future value of annuity'?
What is the primary distinction between the Annual Percentage Rate (APR) and the Effective Annual Rate (EAR)?
What is the primary distinction between the Annual Percentage Rate (APR) and the Effective Annual Rate (EAR)?
Which of the following best describes the term 'm' as used in the formulas for APR and EAR?
Which of the following best describes the term 'm' as used in the formulas for APR and EAR?
If a loan quotes an APR of 10% compounded monthly, what is the value of m in the EAR formula?
If a loan quotes an APR of 10% compounded monthly, what is the value of m in the EAR formula?
Which of the following actions is explicitly discouraged when calculating the period rate?
Which of the following actions is explicitly discouraged when calculating the period rate?
How to calculate the Effective Annual Rate (EAR) with the APR and number of periods per year $m$?
How to calculate the Effective Annual Rate (EAR) with the APR and number of periods per year $m$?
How to calculate the Annual Percentage Rate (APR) with the Effective Annual Rate (EAR) and number of periods per year $m$?
How to calculate the Annual Percentage Rate (APR) with the Effective Annual Rate (EAR) and number of periods per year $m$?
In Excel, which function is used to calculate the effective interest rate when provided with the nominal rate and the number of compounding periods per year?
In Excel, which function is used to calculate the effective interest rate when provided with the nominal rate and the number of compounding periods per year?
In Excel, which function is used to calculate the nominal interest rate when provided with the effective interest rate and the number of compounding periods per year?
In Excel, which function is used to calculate the nominal interest rate when provided with the effective interest rate and the number of compounding periods per year?
Given an APR of 8% compounded quarterly, which calculation allows you to find the EAR?
Given an APR of 8% compounded quarterly, which calculation allows you to find the EAR?
If an investment has an Effective Annual Rate of 10%, and interest is compounded monthly, setup the calculation that finds the Annual Percentage Rate (APR).
If an investment has an Effective Annual Rate of 10%, and interest is compounded monthly, setup the calculation that finds the Annual Percentage Rate (APR).
What is the value of 'npery' in the Excel EFFECT and NOMINAL formulas?
What is the value of 'npery' in the Excel EFFECT and NOMINAL formulas?
If an investment quotes an APR of 12% compounded semi-annually, what is the value of 'm'?
If an investment quotes an APR of 12% compounded semi-annually, what is the value of 'm'?
A loan has an EAR of 7.5%. If the interest is compounded quarterly, what setup would find the APR?
A loan has an EAR of 7.5%. If the interest is compounded quarterly, what setup would find the APR?
Which rate is typically used for time line visualizations and calculations?
Which rate is typically used for time line visualizations and calculations?
Why should one not divide the effective rate by the number of periods per year?
Why should one not divide the effective rate by the number of periods per year?
Flashcards
Present Value
Present Value
The value today of a future cash flow.
Future Value
Future Value
The value of an investment at a future point in time.
Discounting Factor
Discounting Factor
A factor used to calculate the present value of a future cash flow, it accounts for the time value of money.
Discounting
Discounting
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Time and Present Value
Time and Present Value
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Interest Rates and Present Value
Interest Rates and Present Value
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Number of Periods Formula
Number of Periods Formula
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Computing Number of Periods
Computing Number of Periods
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Ordinary Annuity
Ordinary Annuity
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Annuity Due
Annuity Due
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Perpetuity
Perpetuity
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PV of Ordinary Annuity Formula
PV of Ordinary Annuity Formula
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FV of Ordinary Annuity Formula
FV of Ordinary Annuity Formula
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PV of Perpetuities Formula
PV of Perpetuities Formula
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Present or Future Value of Annuity Due
Present or Future Value of Annuity Due
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Number of Periods
Number of Periods
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Loan Repayment Period
Loan Repayment Period
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Monthly Interest Rate
Monthly Interest Rate
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Principal Amount
Principal Amount
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Loan Payment
Loan Payment
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Time Value of Money
Time Value of Money
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Present Value Calculation
Present Value Calculation
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Discount Rate
Discount Rate
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Present Value of Uneven Cash Flows
Present Value of Uneven Cash Flows
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Future Value of Uneven Cash Flows
Future Value of Uneven Cash Flows
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Effective Annual Rate (EAR)
Effective Annual Rate (EAR)
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Annual Percentage Rate (APR)
Annual Percentage Rate (APR)
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APR Calculation
APR Calculation
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Present Value (PV)
Present Value (PV)
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Future Value (FV)
Future Value (FV)
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Key Concepts: PV, FV, Discounting Factor, Discounting
Key Concepts: PV, FV, Discounting Factor, Discounting
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Interest Amount
Interest Amount
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Compounding Periods (m)
Compounding Periods (m)
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Period Rate
Period Rate
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EAR and Period Rate
EAR and Period Rate
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Calculating EAR
Calculating EAR
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Effective Interest
Effective Interest
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Nominal Interest Rate
Nominal Interest Rate
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EFFECT Function in Excel
EFFECT Function in Excel
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NOMINAL Function in Excel
NOMINAL Function in Excel
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EAR vs APR
EAR vs APR
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Compounding Frequency and EAR
Compounding Frequency and EAR
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Comparing Investments
Comparing Investments
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Misleading APR
Misleading APR
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Importance of Compounding
Importance of Compounding
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Study Notes
Module 2: Basic Concepts and Application of Time Value of Money
- Students should be able to explain compounding and bringing the value of money back to the present
- Students should be able to understand annuities
- Students should be able to determine future or present value of a sum when there are non-annual compounding periods.
- Students should be able to determine the present value of an uneven stream of payments, and understand perpetuities
Lecture Outline
- Time value of money
- Using timelines to visualize cash flows
- Compounding and future value
- Discounting and present value
- Computing number of periods
- Present value or future value of annuities, annuities due, and perpetuities
- Computing numbers of periods or interest rates (given variables)
- Future and present value of uneven cash flows
- Comparing interest rates (APRs versus EARs)
- Applications of time value of money
2.1 The concept of time value of money
- Money has time value: a dollar today is worth more than a dollar tomorrow.
- Reasons for time value:
- Immediate use of money
- Investment opportunities and returns
- Inflation
- Cost avoidance
- Risk of loan non-repayment
- Interest rate: exchange rate between earlier money and later money
- Need for a return, given value today versus tomorrow
- Loss of value from other potential uses must be recognized
- Relevant variables in dealing with time value of money:
- Initial amount (principal)
- Time period of the loan
- Interest rate
- Time period to which interest rate applies
2.1 Simple vs. Compound Interest
- Simple interest: applied to the principal for a given time period
- Compounded Interest: interest earned during the first period is added to the principal, then interest is earned on this new sum during the next period.
2.1 Simple vs. Compound Interest Example
- Deposit $500 at 5% annual interest
- Simple Interest: $50 after 2 years; Balance = $550.
- Compound Interest (annually compounding): $51.25 after 2 years; Balance = $551.25
2.2 Using Timelines to Visualize Cash Flows
- Timelines identify timing and amount of cash flows along with interest rate.
- Tick marks occur at the end of periods (years, months, etc.). Time 0 is today
- Timelines are typically expressed in years (also months, days etc).
2.2 Uneven Cash Flow Stream Example
- 3-year timeline with a 10% interest rate shows a $100 outflow at time 0 followed by $100 $75 and $50 inflows at times 1, 2 and 3 respectively.
2.3 Compounding and Future Value
- Future value (FV): Worth of a cash flow in the future
- Example: $1,000 invested at 5% for one year:
- FV = $1,050
- Example: $1,000 invested at 5% for two years:
- FV = $1,102.50 using the compounding formula
2.3 Compounding and Future Value (Excel Function)
- Excel FV function: calculate future value of a sum
2.4 Discounting and Present Value
- Present value: What a future cash flow is worth today.
- Present value and Future Value are mirror images
- Discounting factor: 1 / (1 + r)t where r is the interest rate and t is the number of periods
- Calculating Present Value (using Excel): PV(rate, nper, pmt, fv, type)
2.4 Discounting and Present Value Examples
- $10,000 needed in one year at a 7% interest rate = $9,345.79 today
- $150,000 needed in 17 years at 8% interest rate = $40,540.34 today
- $19,671.51 worth today with a 10-year investment at 7% = $10,000
2.5 Computing Number of Periods
-
Formula for calculating number of periods t -t =ln(FV / PV)/ln(1 + r)
-
Example: $15,000 investment at 10% interest to get $20,000 = 3.02 years
2.6 PV or FV of Annuities, Annuities Due and Perpetuities
- Annuity: Sequence of equal cash flows at the end of each period (Ordinary Annuity)
- Annuity-due: Sequence of equal cash flows at the beginning of each period.
- Perpetuity: Infinite series of equal payments
2.6 Annuities and Perpetuities Basic Formulas
- Ordinary Annuity Present Value
- Ordinary Annuity Future Value
- Perpetuity Present Value
- Calculating PV/FV of annuity-due (multiple formula)
2.6 PV or FV of Annuities, Annuities Due and Perpetuities Examples
- Calculate the present value of $632 monthly payments over 48 months at 1% per month
- Calculate the future value of $10,000 yearly payments over 30 years at 10% per year
- Calculate present value of an annual graduation party that costs $30,000
2.7 Using Excel's Functions to compute one variable given Relevant Variables
- Excel functions for time value of money used
- FV, PV, NPER, RATE, PMT
2.7 Using Excel's Functions to compute one variable given Relevant Variables: Examples
- Calculate monthly payment for a $20,000 loan at 8% annual interest over 4 years.
- Calculate time to pay off a $1000 credit card debt with $20 monthly payments at 1.5% interest rate.
- Calculate interest rate for a $10,000 loan with $207.58 monthly payments over 60 months
2.8 Future and Present Value of Uneven Cash Flows
- Calculate Present Value of Uneven cashflow
- NPV(rate, CF₁, CF₂, ..., CFN) + CF₀
2.8 Future and Present Value of Uneven Cash Flows: Examples
-
Present value of $1500, $1000 and $500 in three years when bank interest is 6%
-
Future value of $1500, $1000 and $500 in three years when the bank interest is 6%
2.9 Comparing Interest Rates: APRs vs EARs
- Effective Annual Rate (EAR): Actual rate after compounding.
- Annual Percentage Rate (APR): Annual rate quoted by law
- APR = Period rate * number of periods per year (used in calculations)
- Example: Calculate APR if 12% effective interest rate with monthly compounding
2.9 Comparing Interest Rates: APRs vs EARs, Examples
- Comparing two savings accounts with different compounding periods:
- Calculate EAR of 21.7% APR with daily compounding.
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