Finance Notes

Suppose you are planning to invest $1,000. You'd like to grow your investment to $2,000. If your investment earns an annual return of 5% compounded monthly, how many years will it take to reach your goal? Round to one decimal place. Equation to remember: n(m)= (ln(FV/PV))/(ln(1+i/m))

13.9

Suppose you will receive $50 each week for 8 years. How much is this worth to you today if your discount rate is 9%? Round to the nearest dollar. Equation to remember: Non-annal PV annuity= CF[(1/(i/m))-(1/((i/m)*(1+i/m)^(n*m))]

14818.0

Suppose you borrow $50,000 for 4 years by taking out an amortized loan at a 9% interest rate. How much are your annual payments? Round to the nearest dollar.Hint: Use Equation 3.2 and solve for the PMT. Equation to remember: (Annual) Principal= PMT[(1/i)-(1/(i)(1+i)^n)]

15433.0

m as the number of compounding periods in a year. For example, if interest compounds semi-annually, m equals ?. Quarterly: m=?. Monthly: m=?. Weekly: m=?. Daily: m=?, and so on.

2 ; 4 ; 12 ; 52 ; 365

What is the US Federal Reserve's inflation target? 0% 1% 2% 5%

2%

Suppose you are planning to deposit $5,000 in a CD account. You'd like your deposit to grow to $6,000 in 8 years. If interest in the account compounds monthly, what annual interest rate do you need? Answer in percent and round to two decimal places. Equation to remember: i/m=([FV/PV]^1/n(m))-1

2.28

FV = PV(1+i)n to this particular context: Balloon payment = Principal x (1+i)^n

Balloon payment = Principal x (1+i)^n Example: Suppose your commercial real estate company borrows $10 million from a bank to help finance the construction of an office building. If the loan has an interest rate of 7% and a term of 3 years, what will be the required balloon payment at the term of the loan? How much interest will you pay the bank (assuming you don't default)? Solution: Since this is a balloon loan with full payment at term, we can use Equation 3.1, with principal = $10 million, i=7%, and n=3. Balloon payment = $10 million x (1+0.07)^3 = $12,250,430 Total interest owed = Total payment ($10 million) - Principal ($12,250,430) = $2,250,430

Which of the following is/are reason(s) money has time value People's time preference Paper money gets physically worn out over time Uncertainty about the future Inflation Opportunity cost

Inflation People's time preference Uncertainty about the future Opportunity cost

All else the same, a balloon loan racks up a greater amount of interest compared to an amortized loan with the same principal, interest rate and time to maturity. True or false? True False

True

Short-term loans and bonds tend to have balloon payments while longer term loans tend to be amortized. True or false? True False

True

T/F Equity refers to an ownership interest in a company.

True

Suppose a question says you will receive a payment of $200 three years from today. Where on the timeline would you put that amount? Under 0 Under 2 Under 3 Under 5

Under 3

Suppose a question says you will receive a payment of $500 at the beginning of year 4. Where on the timeline would you put that amount? Under 0 Under 2 Under 3 Under 4

Under 3

Which of the following institutional investors is the largest owner of Microsoft shares as of June 2022? Fidelity Investments Vanguard Group Blackrock PIMCO Ince Group

Vanguard Group

Week 2

Week 2 cash flows

Match the market activity on the left with the type of market on the right. You are selling 100 shares of Amazon stock you own in your brokerage account Amazon is borrowing by issuing bonds in the bond market Secondary Market Primary Market

You are selling 100 shares of Amazon stock you own in your brokerage account- Secondary Market Amazon is borrowing by issuing bonds in the bond market- Primary Market

Equation to remember: I= ?

[FV/PV]^(1/n)-1 Example: Suppose you deposited $100 in a savings account. If you have $124 in the account after 5 years, what interest rate did you earn on your savings? Answer in percentage and round to two decimal places. Solution: Since we know the initial deposit, the final amount in the account and the time between the two, we can find the interest rate using Equation 2.3: i = [124/100]^(1/5) - 1 = 0.04396 = 4.40%

A high-net-worth individual who provides financial backing for small startups or entrepreneurs, typically in exchange for ownership equity in the company is called a ________ investor.

angel

Information _____ occurs when one party to a transaction has more information than the counterparty.

asymmetry

Financial institutions which provide both commercial and investment banking operations under one roof are called _____ banks.

universal

Debt that is not backed by collateral is called _____ debt.

unsecured

The idea that management should aim to maximize its share price is known as shareholder _____ maximization or shareholder primacy.

value

The process of transforming loans into tradable bond-like securities is called _____.

securitization

Corporate social responsibility is also known as the principle of _____ value.

stakeholder

Amortized Loans Principal=

(Annual) Principal= PMT[(1/i)-(1/(i)(1+i)^n)] Example: Suppose the loan in Example 3.1 was structured as an amortized loan instead. What would the annual payments have to be? How much interest would you owe the bank in that case? Solution: Using Equation 3.2 with principal of $10 million, interest rate of 7%, and term of 3 years: $10 million= PMT [(1/.07)-(1/(.07)(1+.07)^3)]= PMT x 2.624316044 ~= PMT ~= $10 million/2.624316044 ~= $3,810,516.66 You would have to make three annual payments of a little over $3.8 million each for three years. Total interest owed = Total payments - Principal = 3 x $3,810,516.66 - $10 million = $1,431,549.97

Effective annual interest rate (EAR)= ?

(EAR)= ((1+(i/m))^m)-1

Which of the following are correct about bonds? Select all that apply. -Bonds are financial securities that trade in the bond market. -Bonds are more restrictive for the borrower compared to loans. -Bonds are typically sold to one or a few large institutional investors. -The bond market is typically for larger and more established borrowers.

-Bonds are financial securities that trade in the bond market. -The bond market is typically for larger and more established borrowers.

Consider a monthly annuity and an interest rate of 2.4%. What is the periodic (monthly) interest rate? Answer in percent. Equation to remember: Periodic interest rate= i/m

.2

Suppose the annual interest rate is 3.5% compounded monthly. What is the monthly (periodic) interest rate? Answer in percent rounded to two decimal places. Equation to remember= i/m

0.29

If I deposit $10,000 into an account earning an interest rate of 1.5%, how much will I have in the account after 10 years? Round to the nearest cent (two decimal places, no $ sign) Equation to remember: FV= PV(1+i)^n

11605.41

What is the future value of $100,000 after 8 years earning 3% compounded monthly? Round to the nearest whole number. Equation to remember: FV=PV((1+(i/m))^n(m))

127087.0

You expect to receive 7 annual cash flows of $3,000 each followed by a single payment of $10,000 at the end of year 8. If the discount rate is 7%, what is the present value of this combined annuity? Round to the nearest dollar. Hint: This combines an annuity and a single cash flow. Steps: Find the PV of an annuity with CF=$3,000, i=7% and n=7. Find the PV of a single cash flow with FV=$10,000, i=7%, and n=8. Calculate the sum of the PVs. Equation to remember: Present Value Combined Annuities

21989.0

Suppose you deposit $50 each week into an account earning 3% interest for 8 years. How much will you have at the end? Round to the nearest dollar. Equation to remember: Non-annual FV annuity= CF[((1+i/m)^n(m))-1)/(i/m)]

23501.0

What's the effective annual rate (EAR) of a credit card that charges an annual interest rate of 24% compounded daily? Answer in percent rounded to one decimal place. Equation to remember: (EAR)= ((1+(i/m))^m)-1

27.1

Consider a weekly annuity for 6 years. How many cash flows will there be in total? Equation to remember: Number of compounding periods= n(m)

312

If you would like to have $50,000 in 10 years by investing in an account earning 4% compounded weekly, how much do you need to deposit today? Round to the nearest whole number. Equation to remember: PV= FV/((1+i/m)^n(m))

33521.0

You invest $3,000 each year for 10 years and earn a rate of return of 4%. How much will you have after 10 years? Round to the nearest dollar. Equation to remember: Annual FV annuity= CF((1+i)^n)-1)/i

36018

Suppose you deposited $1,000 in a savings account. If you have $1,385 in the account after 7 years, what annual interest rate did you earn on your savings? Answer in percentage and round to two decimal places. (do not include the % sign in your answer) Equation to remember: I= [FV/PV]^(1/n)-1

4.76

What is the present value of annual cash flows of $6,000 for 12 years if the discount rate is 10%? Round to the nearest dollar. Equation to remember: Annual PV annuity= CF[(1/i)-(1/i*(1+i)^n)]

40882

Suppose you have $30,000 in a savings account earning 2.4%. You would like to make equal monthly withdrawals from this account for the next 6 years to sustain your living expenses in college. What's the most you can withdraw? Round to the nearest dollar. Equation to remember: Solving for cash flows Non-annal or PV annuity= CF[(1/(i/m))-(1/((i/m)*(1+i/m)^(n*m))] then you divide the amount you "supposedly have" by [(1/(i/m))-(1/((i/m)*(1+i/m)^(n*m))] to get CF.

448.0

Consider a deferred annuity with 8 annual payments of $1,000 starting at the end of year 5. If the discount rate is 6%, what is the present value of this deferred annuity? Round to the nearest dollar. Hint: The first cash flow is at t=5. The PV annuity formula will give you the discounted value of this annuity as of one period before the first cash flow, which is t=4. Then, you need to discount the PV annuity you calculated back 4 more years to t=0. Steps: Calculate PV annuity with CF=$1,000, i=6% and n=8. Discount the value from step 1 from t=4 back to t=0 using the PV of a single cash flow formula with i=6% and n=4. Equation to remember: Present value deferred annuity

4919.0Z

What is the present value of $300 to be received at the end of each year in perpetuity? Assume a discount rate of 6%. Round to the nearest dollar. Equation to remember: PV= CF/i

5000

You'd like to save $2 million. How much should you save each year for the next 20 years in order to reach this goal? Assume your savings will earn a 5% annual return. Round to the nearest dollar. Equation to remember: Solving for cash flows Non-annual or FV annuity= CF[((1+i/m)^n(m))-1)/(i/m)] you then divide the end value by [((1+i/m)^n(m))-1)/(i/m)] to get CF.

60485.0

Suppose you are looking to buy a car for $40,000. You will pay for it by taking out a car loan at 1.5% interest and a 5-year term. The down payment is 10%. What are your monthly payments? Round to the nearest dollar. Hint: Since payments are monthly, m=12 and you need to use Eq. 3.3 to solve for the PMT. Don't forget the down payment, which comes out of your pocket. The loan principal is 90% of the purchase price. Equation to remember: (Non-Annual) Principal= PMT[(1/(i/m)-(1/(i/m)(1+i/m)^n(m))]

623.0

If I deposit $8,000 into an account earning 2% interest, how much interest will I earn over the next 4 years? Round to the nearest cent. Equation to remember: Interest earned= FV-PV

659.46

Suppose you borrow $50,000 for 4 years by taking out a balloon loan at a 9% interest rate. How much do you need to pay back when the loan matures in 4 years? Round to the nearest dollar. Equation to remember: Balloon payment = Principal x (1+i)^n

70579.0

You are expecting to receive two payments: $5,000 in one year and $3,000 in two years from today. What is the total present value if your discount rate is 6%? Round to the nearest dollar. Equation to remember: PV of a series of cash flows with annual compounding= ((CF downwards carrot 1)/(1+i))+((CF downwards carrot 2)/((1+i)^2))+...+((CF downwards carrot T-1)/((1+i)^T-1))+((CF downwards carrot T)/((1+i)^T))

7387

Suppose you deposited $1,000 into a savings account earning 2.1% interest. How long will it take for the balance to grow to $1,200? Answer in years rounded to one decimal place. Equation to remember: N= ln(FV/PV)/ln(1+i)

8.8

You are planning to make two deposits into an account earning 2% interest: $5,000 in one year and $3,000 in two years from today. What will the account balance be by the end of year 4? Round to the nearest dollar. Formula to remember: FV of a series of cash flows with annual compounding= (CF downwards carrot 1)(1+i)^(T-1))+(CF downwards carrot 2)(1+i)^(T-2))+(CF downwards carrot T-1)(1+i)^(1))+(CF downwards carrot T)

8427

What is the present value of $14,000 to be received in 8 years if your discount rate is 5%? Round to the nearest cent. Equation to remember: PV= FV/(1+i)^n

9475.75

The notion that the shareholders of a corporation are not directly involved in the company's management is called the _____ of ownership and management.

separation

Annual PV annuity=

Annal PV annuity= CF[(1/i)-(1/i*(1+i)^n)] Example: Someone will pay you $5,000 each year for 5 years. How much is that worth to you today if the appropriate discount rate is 7%? Solution: Before we use the new annuity formula, let's do it the old way. Let's compute the PV of each cash flow separately using Equation 2.2 and add them up. Recall the formula for the PV of a single cash flow provided by Equation 2.2: PV = FV / (1+i)n So, breaking this annuity down: Cash flow 5: PV = $5,000 / (1+0.07)5 = $3,564.93 Cash flow 4: PV = $5,000 / (1+0.07)4 = $3,814.48 Cash flow 3: PV = $5,000 / (1+0.07)3 = $4,081.49 Cash flow 2: PV = $5,000 / (1+0.07)2 = $4,367.19 Cash flow 1: PV = $5,000 / (1+0.07)1 = $4,672.90 Total PV of this annuity = $20,500.99, which is the sum of all these cash flows in present value. ​Now, let's use Eq 2.11 with CF=$5,000, n=5 and i=0.07 PV annuity= 5000[(1/0.07)-(1/0.07*(1+i0.07^5)]= the same $20,500.99

If not stated, compounding frequency must be Daily Monthly Weekly Annual

Annual

Annual FV annuity=

Annual FV annuity= CF((1+i)^n)-1)/i Example: You invest $5,000 each year for 5 years (at the end of the year) and earn an interest rate of 2.4%. How much will you have in total after 5 years? Solution: Recall the formula for the FV of a single cash flow given by Equation 2.1: FV = PV(1+i)n Cash flow 1: FV = $5,000(1+0.024)4 = $5,497.56 Cash flow 2: FV = $5,000(1+0.024)3 = $5,368.71 Cash flow 3: FV = $5,000(1+0.024)2 = $5,242.88 Cash flow 4: FV = $5,000(1+0.024)1 = $5,120.00 Cash flow 5: FV = $5,000 Total FV of this annuity = $26.229.15, which is the sum of the future value of all of these cash flows as of the end of year 5. Shortcut: Substitute CF=$5,000, n=5, and i=0.024 into Eq FV annuity= $5,000((1+0.024)^5)-1)/i Total FV of this annuity = $26.229.15

Match compounding frequency on the left with the correct m value on the right Annual Semi-annual Weekly Monthly Daily m = 1 m = 12 m = 52 m = 2

Annual: m = 1 Semi-annual: m = 2 Weekly: m = 52 Monthly: m = 12 Daily: m = 365

CH 3

CH3

Which of the following financial intermediaries' primary function is to collect deposits and make loans? Investment banks Investment managers Brokers Commercial banks

Commercial banks

Present Value Combined Annuities

Example: Find the present value of the following stream of cash flows: i= 7% Year 0= Year 1= $5000 Year 2= $5000 Year 3= $5000 Year 4= $5000 Year 5= $9000 Let's first dissect this timeline into its individual parts. One way to look at it is as an annuity with 4 annual payments of $5,000 combined with a single cash flow of $9,000 at the end of year 5. Now what do we do? Step 1: Get rid of the annuity by converting its to its single cash flow equivalent. Here we do this by calculating its present value since this is what the question is asking us. Using Equation 2.11 with CF = $5,000, i = 0.07 and n = 4: PV Annuity= $5,000[(1/0.07)-(1/(0.07((1+0.07)^4))]= $16,936.06 Here's the trick. We can think of that annuity as if it is a single cash flow of $16,936.06 received at time zero. The two are financially equivalent. So we have now transformed the timeline to the following version that is easier to handle: i= 7% Year 0= $16,936.06 Year 1= Year 2= Year 3= Year 4= Year 5= $9000 So now we have only two single cash flows left to deal with. Step 3: Let's now move all remaining single cash flows to the desired point in time (in this case time zero) using the formulas for single cash flows and add them up. Since the first single cash flow is already at time zero, we only need to discount the $9,000 from year 5 using Equation 2.2: PV= FV/(1+i)^n = $9,000/(1+0.07)^5= $6,416.88 Now that all values are at the same point on the timeline, we can add them up. Total PV = $16,936.06 + $6,416.88 = $23,352.94

Solving for cash flows Non-annal or PV annuity= CF[(1/(i/m))-(1/((i/m)-(1+i/m)^(n*m))] then you divide the amount you "supposedly have" by [(1/(i/m))-(1/((i/m)*(1+i/m)^(n*m))] to get CF.

Example: Suppose you have $10,000 in a savings account earning 2.1%. You would like to make equal monthly withdrawals from this account for the next 3 years to sustain your living expenses in college. What's the most you can withdraw? "What's the most you can withdraw?" is our clue that this is a "solve for CF" problem. Solution: CF= [1/(0.021/12)-1/(0.021/12)(1+(0.021/12))^(3(12)) We know that this equals $10,000. We can solve for CF by dividing both sides by the term to the right of CF: then to find CF divide $10,000 by [1/(0.021/12)-1/(0.021/12)(1+(0.021/12))^(3(12)) =The answer is CF = $286.86 per month. If we withdraw that amount each month and continue to earn 2.1% on our remaining savings, our initial $10,000 will last us exactly 3 years and by the end we will have reached an account balance of zero with the very last (36th) monthly withdrawal.

Solving for cash flows Non-annual or FV annuity= CF[((1+i/m)^n(m))-1)/(i/m)] you then divide the end value by [((1+i/m)^n(m))-1)/(i/m)] to get CF.

Example: You'd like to save $1 million. How much should you save each year for the next 15 years in order to reach this goal? Assume your savings will earn a 7% annual return. "How much should you save each year?" is our clue that this is a "solve for CF" problem. We know that this equals $1 million. We can solve for CF by dividing both sides by the term to the right of CF: Solution: CF=(((1+0.07)^15) -1)/0.07 then to find CF divide $1 million by (((1+0.07)^15) -1)/0.07 =The answer is CF = $39,794.62 per year. If we save that amount at the end of each year for 15 years and earn 7% on our savings, evidently we will end up with $1 million in 15 years.

FV of a series of cash flows with annual compounding:

FV of a series of cash flows with annual compounding: (CF downwards carrot 1)(1+i)^(T-1))+(CF downwards carrot 2)(1+i)^(T-2))+(CF downwards carrot T-1)(1+i)^(1))+(CF downwards carrot T) Example 1: You are planning to deposit $1,000 in an account at the end of each year for three years starting one year from today. If the account earns 7% interest, what will the account balance be by the end of year 3? Solution Example 1: FV=($1,000((1+0.07)^2))+($1,000((1+0.07)^1))+$1,000=$3,214.90

Equation to remember: Interest earned= ?

FV-PV FV= Future value PV= Present value Example: If I invest $5,000 today, how much will it be worth in 1 year given an interest rate of 2.4%? How much interest will I have earned? Using Equation 2.1, FV = $5,000 (1+0.024)^1 = $5,120 Interest earned = FV - PV = $5,120 - $5,000 = $120

Equation to remember: PV= ?

FV/(1+i)^n FV= Future value PV= Present value i= discount rate n= number of periods Example: If I expect to receive $3,000 in 5 years, how much is that worth to me today given a discount rate of 8%? Round to the nearest cent. Using Equation 2.2, PV = $3,000 / (1+0.08)^5 = $2,041.75

FV of a single cash flow with non-annual compounding

FV=PV((1+(i/m))^n(m)) Example: What is the future value of $10,000 after 10 years of earning 4% compounded weekly? Solution: Compounded weekly means m = 52. The periodic rate is i/m = 4%/52 = 0.07692%. This weekly interest will be earned for n x m = 10 x 52 = 520 compounding periods. Using Equation 2.5, FV = $10,000 (1 + 0.04/52)10x52 = $14,915.95

CFPB stands for the Consumer_____ _____ Bureau.

Financial Protection

You'd like to save $2 million. You are trying to figure out how much you should save each year for the next 20 years in order to reach this goal. Is $2 million the future or present value of the annual savings you are considering? Present value Future value

Future value

Sort the following categories of goods and services by the increase in the price index since 2001, from highest to lowest. Software Food Childcare TVs New cars Hospital services College tuition

Hospital services College tuition Childcare Food New cars Software TVs

Present value deferred annuity

Let's find the current value of the deferred annuity above. i= 7% Year 0= Year 1= Year 2= -> PV annuity Year 3= $5000 Year 4= $5000 Year 5= $5000 Year 6: $5000 Year 7: $5000 -> FV annuity Step 1: Convert the annuity to its single cash flow equivalent using Eq 2.11. Note that n=5 since there are five annual cash flows. PV Annuity= $5,000[(1/0.07)-(1/(0.07((1+0.07)^5))]= $20,500.99 Step 2: Put that value at the right place on the timeline (one period before first cash flow, so t=2) i= 7% Year 0= Year 1= Year 2= $20,500.99 -> PV annuity Year 3= $5000 Year 4= $5000 Year 5= $5000 Year 6: $5000 Year 7: $5000 Step 3: Now we need to move the discounted value of the deferred annuity to the desired point in time (in this case year 0) using the formulas for single cash flows. Using Equation 2.2 for the present value of a single cash flow with FV=$20,500.99, n = 2, and i=7%: PV = $20,500.99 / (1 + 0.07)2 = $17,906.36

Future Value Combined Annuities

Let's work with the same timeline as in the previous example. But this time let's find the future value of those cash flows as of year 7. i= 7% Year 0= Year 1= $5000 Year 2= $5000 Year 3= $5000 Year 4= $5000 Year 5= $9000 Year 6: Year 7: Solution: Again, we approach this in three steps. Step 1: Convert the annuity to a single value. Here we do this by calculating its future value since this is what the question is asking us. Using Equation 2.10, with CF = $5,000, i = 0.07 and n = 4: FV annuity: $5,000[(((1+0.07)^4)-1)/0.07]= $22,199.72 Step 2: Now, the important question is this: Where on the timeline does this FV belong? Recall the timing of annuity formulas: FV annuity value goes where the last annuity cash flow is. So, the annuity in this example can be replaced by FV annuity as a single cash flow occurring at year 4. i= 7% Year 0= Year 1= Year 2= Year 3= Year 4= $22,199.72 Year 5= $9000 Year 6: Year 7: Step 3: We have only single cash flows left. Now we move them to the desired point in time (in this case year 7) using the formulas for single cash flows and add them up. We need to compound FV annuity from the previous step for 3 years (year 4 to year 7) and $9,000 for 2 years (year 5 to year 7) with i = 7% using Equation 2.1: FV = PV(1+i)n. FV = $22,199.72 (1 + 0.07)^3 + $9,000 (1 + 0.07)^2 = $37,499.71

Match the corporate characteristic on the left with the correct definition on the right Limited liability Joint-stock ownership Corporate personhood Trading of company's shares by shareholders does not affect the company's continued existence Investors are not personally liable for the company's obligations The corporation is a separate legal entity from its shareholders with its own rights and obligations

Limited liability- Investors are not personally liable for the company's obligations Joint-stock ownership- Trading of company's shares by shareholders does not affect the company's continued existence Corporate personhood- The corporation is a separate legal entity from its shareholders with its own rights and obligations

Finance first emerged in the early urban civilizations of _____.

Mesopotamia

Equation to remember: N= ?

N= ln(FV/PV)/ln(1+i)

Future value deferred annuity

No example

Non-annal PV annuity=

Non-annal PV annuity= CF[(1/(i/m))-(1/((i/m)*(1+i/m)^(n*m))]

Non-annual FV annuity=

Non-annual FV annuity= CF[((1+i/m)^n(m))-1)/(i/m)]

Number of compounding periods=

Number of compounding periods= n(m) Multiply the number of years (n) by m, which gives us the number of compounding periods, nxm.

The Chief _____ Officer is responsible from managing the company's day-to-day operations and implementing the CEO's vision.

Operating

PV of a series of cash flows with annual compounding:

PV of a series of cash flows with annual compounding: ((CF downwards carrot 1)/(1+i))+((CF downwards carrot 2)/((1+i)^2))+...+((CF downwards carrot T-1)/((1+i)^T-1))+((CF downwards carrot T)/((1+i)^T)) Example 1: Suppose someone promised to pay you $1,000 each year for 3 years starting at the end of year 1. What is this stream of cash flows worth to you today if the discount rate is 7%? Solution 1: PV=($1,000/1+0.07)+($1,000/(1+0.07^2))+($1,000/(1+0.07^3))=$5,130.35 Example 2: Suppose someone promised to pay you $1,000 every other year, starting at the end of year 2, until the end of year 10. What is the present value of this cash flow stream (i.e., how much would you be willing to pay today for this cash flow stream)? Assume discount rate of 7%. We need to discount the first $1,000 for 2 years, the second one for 4 years, so on: Solution2: PV=($1,000/(1+0.07^2))+($1,000/(1+0.07^4))+...+($1,000/(1+0.07^10))=$3,393.03

Equation to remember: FV= ?

PV(1+i)^n FV= Future value PV= Present value i= interest rate n= number of periods

PV=

PV= CF/i Example: What is the present value of $1,000 to be received at the end of each year forever? Assume a discount rate of 10%. Solution: Using Equation 2.14, PV = $1,000 / 0.1 = $10,000

PV of a single cash flow with non-annual compounding

PV= FV/((1+i/m)^n(m)) Example: If I want to accumulate $30,000 in 8 years by investing in an account earning 5% compounded monthly, how much do I need to deposit today? Solution: First we need to decide in which direction we need to go in time. Since we are looking for the amount of deposit needed today for a given future value, we need to go back in time, meaning that this is a discounting problem where we are seeking the present value of a future cash flow. Since we need to find the present value of a single cash flow with non-annual compounding, we need to use Equation 2.6 with the correct compounding frequency. Compounded monthly means m = 12. Using Equation 2.6, PV = $30,000 / (1 + 0.05/12)8x12 = $20,126.32 We would have to deposit $20,126.32 in order to accumulate $30,000 in 8 years.

Periodic Rate=

Periodic Rate= i/m

Periodic interest rate=

Periodic interest rate= i/m Divide the annual interest rate (i) by m, which gives us the periodic rate, i/m.

The type of financial fraud where early investors are paid with the investments of later investors is called a______ scheme.

Ponzi

Suppose you have $30,000 in a savings account. You are trying to figure out how much you can withdraw from this account each month for the next 6 years. Is $30,000 the future or present value of the monthly withdrawals? Present value Future value

Present value

non-annual payments Principal=

Principal= PMT[(1/(i/m)-(1/(i/m)(1+i/m)^n(m))] Example: You are about to buy a $350,000 house. You plan to make a 20% down payment and borrow the rest. A mortgage lender offers a 4% fixed rate loan for 30 years. If you go with this loan, how much will your monthly payments be? How much interest will you pay over those 30 years? Solution: 20% down payment means you will pay 20% of the purchase price now and the rest will be the loan's principal. So, Principal = Purchase price x (1 - Down payment)= $350,000 x (1- 0.2) = $280,000 Plugging all the numbers in Equation 3.3: $280,000= PMT [(1/(.4/12)-(1/(.4/12)(1+.4/12)^30(12))] ⇒PMT ≅ $280,000 / 209.4612404 ​≅ $1,336.76 each month for 360 months​ Total interest = Total payments - Principal = 360 x $1,336.76 - $280,000 = $201,234.62

SEC stands for the_____ and_____ commission.

Securities ; Exchange

_____ refers to equity that is traded in financial markets.

Stock

compounding periods= ?

compounding periods= n(m) Multiply the number of years (n) by m, which gives us the number of compounding periods, nxm. For example, $1 earning interest quarterly for three years is compounded a total of 3 x 4 = 12 times.

CPI refers to _____ _____ index.

consumer price

The board of _____ sets the strategic direction of a corporation and oversees its performance.

directors

The rate we use to translate future cash flows into present value is called the _____ rate.

discount

An annuity is a stream of regular cash flows at regular intervals, occurring at the ______ of each period. beginning end

end

If a problem doesn't specify when the payments are made/received, you need to assume they are made at the ______ of each period. beginning end

end

Corporate _____ refers to the structure of rules, practices, and processes used to direct and manage a company.

governance

"Solve for i" with non-annual compounding

i/m=([FV/PV]^1/n(m))-1 Example: Suppose you are planning to deposit $10,000 in a CD account. You'd like your deposit to grow to $12,000 in 4 years. If interest in the account compounds weekly, what annual interest rate do you need? Answer in percentage and round to two decimal places. Solution: We are looking for the interest rate with non-annual compounding, so we need to use Equation 2.7. Since interest compounds weekly, m = 52. (Important: With periodic interest rates, we are working with some very small numbers. Make sure you leave enough decimal places to prevent a rounding error later. Or even better, leave the intermediate answers in the calculator's memory.) This is the periodic (in this case, weekly) interest rate. We are asked to find the annual rate, i. So, we need to move the m in the denominator on the left side to the right side by multiplying the periodic rate we found above by m: i = 52 x 0.0008769 = 0.04560 = 4.56%

The practice of using non-public information to make trades on securities is called_____ trading and is illegal in most countries including the U.S.

insider

Consider $1,000 to be received sometime in the future. An individual with a high time preference would place a _______ value on it today than an individual with a low time preference. greater lower

lower

"Solve for n" with non-annual compounding

n(m)= (ln(FV/PV))/(ln(1+i/m)) Example: Suppose you are planning to deposit $10,000 in a CD account. You'd like your deposit to grow to $12,000. If the interest rate is 3% compounded monthly, how long will it take to reach your target? Answer in years rounded to one decimal place. Solution: This is a "solve for n" problem with non-annual compounding, so we need to use Equation 2.8. Compounding is monthly, which means m = 12: n times m is the total number of periods, which, in this case, is the number of months. We are asked to find the number of years, n. So we need to divide n x m we found above by m: n = 73.01975 / 12 = 6.1 years

periodic rate= ?

periodic rate= i/m Divide the annual interest rate (i) by m, which gives us the periodic rate, i/m For example, if the annual interest rate is 4%, then the semi-annual rate is 4%/2 = 2%. The quarterly rate is 4%/4 = 1%.