Finance Exam 1

How much interest can be accumulated during one year on a $1,000 deposit paying continuously compounded interest at an APR of 10%?

Interest = PV*e^n-PV = $1,000 * e^1 - $1,000 = MATH DOESNT CHECK =$105.17

How much interest will be earned in an account into which $1,000 is deposited for one year with continuous compounding at a 13% rate?

Interest Earned = PV x e^(r) - PV IE = $1,000e^(.13) - $1,000 = 138.83

When an investment pays only simple interest, this means:

Interest is only earned on the original investment.

You're read to make the last of four equal, annual payments on a $1,000 loan with a 10% accrued interest rate. If the amount of the payment is $315.47, how much of that payment is accrued interest?

Interest on payment: PMT - (PMT/(1 + r)) =$315.47 - ($315.47/1.1) = $26.68

A mortgage loan is an example of an amortizing loan. "Amortizing" means that part of the monthly payment is used to pay interest on the loan and part is used to reduce the amount of the loan.

True

A perpetuity is a special form of an annuity.

True

Accrued interest declines with each payment on an amortizing loan.

True

An annuity due must have a present value at least as large as an equivalent ordinary annuity.

True

Compound interest pays interest for each time period on the original investment plus the accumulated interest

True

The discount factor is used to calculate the present value of $1 received in year t.

True

The more frequent the compounding the higher the future value, other things equal.

True

To calculate present value, we discount the future value by some interest rate, r, the discount rate.

True

When money is invested at compound interest, the growth rate is the interest rate.

True

You should never compare cash flows occurring at different times without first discounting them to a common date.

True

A firm decides to pay for a small investment project through 1 million increase in short term bank loans. This is best described as an example of a:

financing decision (they deal with short term loans)

Nominal dollars refer to the amount of purchasing power.

False (Nominal dollars measure the dollar value of a product at the time it was produced.)

An annual percentage rate (APR) is determined by annualizing the rate using compound interest.

False (Solve for the monthly payment. Calculate the rate using the payment you just calculated and your "amount financed.")

The appropriate manner of adjusting for inflationary effects is to discount nominal cash flows with real interest.

False (The real price in a given month is calculated by dividing the nominal price (the price observed in the market) by the CPI (consumer price index) of that month, where the CPI is expressed as a ratio and not a percentage)

Maximizing profits is the same as maximizing the value of a firm- True or false?

False, profit doesn't talk about the other underlying factors that bring value to the firm

An annuity factor represents the future value of $1 that is deposited today.

False: An annuity factor is a financial value that, when multiplied by a periodic amount, shows the present or future value of that amount.

A credit card account that charges interest at the rate of 1.25% per month would have an annually compounded rate of ________ and an APR of ________.

Annually compounded rate: (1+.0125)^12 - 1 = 16.07% APR: (1.25)(12)= 15%

The present value of an annuity stream of $100 per year is $614 when valued at a 10% rate. By approximately how much would the value change if these were annuities due?

Annuity Due: PMT(1+r) - PMT (Annuity due is RIGHT NOW so just times the payment by the rate plus 1) = $614(1.1) - $614 = $61.4

The present value of a perpetuity can be determined by:

Dividing the payment by the interest rate

What is the future value of $10,000 on deposit for 5 years at 6% simple interest?

FV = PV + (PV * r * t) = $10,000+($10,000*.06*5) = $13,000

If inflation in Wonderland averaged about 20% per month in 2000, what was the approximate annual inflation rate?

(1+r)^n-1 = (1+.2)^20 - 1 =791%

What is the annually compounded rate of interest on an account with an APR of 10% and monthly compounding?

(1+r)^n-1=Annually compounded rate of interest Where r is divided by 12 ((1+(.1/12))^12)-1= 10.47%

What is the minimum nominal rate of return that you should accept if you require a 4% real rate of return and the rate of inflation is expected to average 3.5% during the investment?

1 + real rate = ((1+nom)/(1+inflation)) 1 + .04 = ((1+nom)/(1+.035)) =7.64%

A stream of equal cash payments lasting forever is termed:

A perpetuity

Which of the following forms of compensation is most likely to align the interests of managers and shareholders?

A salary that is paid partly in the form of the company's shares

If interest is paid m times per year, then the per-period interest rate equals the:

Annual percentage rate divided by m

Which of the following factors is fixed and thus cannot change for a specific perpetuity?

Cash payment of a perpetuity

An APR will be equal to an effective annual rate if:

Compounding occurs annually

Which of the following will increase the present value of an annuity, other things equal?

Decreasing the interest rate

Agency problems can best be characterized as:

Differing incentives between managers and owners

In calculating the present value of $1,000 to be received 5 years from today, the discount factor has been calculated to be .7008. What is the apparent interest rate?

Discount Factor = 1/(1+r)^n .7008=1/(1+r)^5 =7.37%

What is the discount factor for $1 to be received in 5 years at a discount rate of 8%?

Discount Factor = PV/[(1+r)^n] =1/(1.08)^5 =.6806

What is the APR on a loan with an effective annual rate of 15.01% and weekly compounding interest?

EAR=((1+(APR)/r))^n) - 1 .1501 = (1 + (APR/52))^52 -1 1.1501 = (1 + (APR/52))^52 APR = 14%

What is the effective annual interest rate on a 9% APR automobile loan that has a monthly payments?

EAR=((1+(APR/r))^n) - 1 EAR = ((1+(.09/12))^12 - 1 EAR = 9.38%

An interest rate that has been annualized using compound interest is termed the:

Effective annual interest rate

Assume the total expense for your current year in college equals $20,000. Approximately how much would your parents have needed to invest 21 years ago in an account paying 8% compounded annually to cover this amount?

FV = PV (1+r)^n 20,000 = PV(1.08)^21 =3,973.15

Approximately how long must one wait (to the nearest year) for an initial investment of $1,000 to triple in value if the investment earns 8% compounded annually?

FV = PV(1+r)^n $3,000 = $1,000(1+.08)^n Divide both sides by $1,000 3=(1.08)^n ln(3) = ln(1.08)^n --> ln(3) = n*ln(1.08) n = ln(3)/ln(1.08) = about 14 years

How much interest is earned in just the third year on a $1,000 deposit that earns 7% interest compounded annually?

FV = PV(1+r)^n (It's asking for JUST THE THIRD YEAR) Year 3: $1,000(1+.07)^3 = $1,225.04 Year 2: $1,000(1+.07)^2 = $1,440.90 $1,225.04 - $1,440.90 = $80.14

How much will accumulate in an account with an initial deposit of $100 and which earns 10% interest compounded quarterly for 3 years?

FV = PV(1+r)^n FV = $100(1+(.10/4))^(3*4) FV = $100 (1.025)^12 = $134.49

What will be the approximate population of the U.S. if its current population of 300 million grows at a compound rate of 2% annually for 25 years?

FV = PV(1+r)^n FV = 300,000,000(1.02)^25 =492,181,798

How much more would you be willing to pay today for an investment offering $10,000 in 4 years rather than the normally advertised 5-year period? Your discount rate is 8%.

FV=PV(1+r)^n $10,000=PV(1.08)^4 --> PV=7,350.30 vs $10,000=PV(1.08)^5 --> PV=6,805.83 $7350.30-$6805.83= $544.47

What is the present value of $100 to be deposited today into an account paying 8% compounded semi-annually for 2 years?

FV=PV(1+r)^n $100=PV(1+(.08/2))^(2/2) $100=PV(1.04)^0 =$100

What is the present value of your trust fund if it promises to pay you $50,000 on your 30th birthday (7 years from today) and earns 10% compounded annually?

FV=PV(1+r)^n $50,000 = PV (1.10)^7 =$25,657.91

A corporation has promised to pay $1,000 20 years from today for each bond sold now. No interest will be paid on the bonds during the 20 years, and the bonds are discounted at a 7% interest rate. Approximately how much should an investor pay for each bond?

FV=PV(1+r)^n FV= 1000(1.07)^20 = $3,869.68 $1,000/$3,869.68 = .25842 = $258.42

How much must be deposited today in an account earning 6% annually to accumulate a 20% down down payment to use in purchasing a car one year from now, assuming that the car's current price is $20,000 and inflation will be 4%.

FV=PV(1+r)^n First calculate inflation of car: $20,000(.04)= $800 Calculate car value: $20,000+$800=$20,800 Then calculate how much down you need: $20,800(.20)=$4,160 Then solve: $4,160=PV(1.06)^1 =$3,925

What is the present value of the following payment stream, discounted 8% annually: $1,000 at the end of year 1, $2,000 at the end of year 2, and $3,000 at the end of year 3?

FV=PV(1+r)^n --> PV=FV/(1+r)^n 1. $1,000/(1.08)^1 = $925.90 2. $2,000/(1.08)^2 = $1714.67 3. $3,000/(1.08)^3 = $2381.49 PV = 925.90+1714.67+2381.49 =$5,022.11

How much must be saved annually, beginning 1 year from now, in order to accumulate $50,000 over the next 10 years, earning 9% annually?

FVAF = PMT[(((1+r)^n)-1)/r) [BEGINNING ONE YEAR FROM NOW) $50,000 = PMT [(((1+.09)^10-1)/.09) =$3291

A dollar tomorrow is worth more than a dollar today.

False

An effective annual rate must be greater than an annual percentage rate.

False

Any sequence of equally spaced, level cash flows, is called an annuity. An annuity is also known as a perpetuity.

False

Converting an annuity to an annuity due decreases present value.

False

For a given amount, the lower the discount rate, the less the present value.

False

The present value of an annuity due equals the present value of an ordinary annuity times by the discount rate (PV annuity due = PV ordinary annuity X discount rate)

False: Present value of an annuity is on formula sheet.

Which of the following statements best distinguishes the difference between real and financial assets?

Financial assets represent claims to income that is generated by real assets

Which of the following strategies will allow real retirement spending to remain approximately equal, assuming savings of $1,000,000 invested at 8%, a 25 year horizon, and 4% expected inflation?

First find "real rate" because inflation: Real Rate = [(1+Nominal Rate)/(1+Inflation)] - 1 =(1.08/1.04)-1 = .0385 PVAF = PMT[(1/r)-(1/r(1+r)^n)] $1,000,000 = PMT[(1/.0385)-(1/.0385(1.0385)^25] = about $63,000 annually

If the future value of an annuity due = $25000 and $24000 is the future value of an ordinary annuity that is otherwise similar to annuity due, what is the implied discount rate?

Future Value Annuity Due = Future Value Ordinary Annuity (1+r) 25,000 = 24,000 (1+r) 1,000 = 24,000r r=4.17%

Assume your uncle recorded his salary history during a 40-year career and found that it had increased 10 fold. If inflation averaged 4% annually during the period, how would you describe his purchasing power on average?

He "beat" inflation by slightly below 2% annually

Given as a set future value, which of the following will contribute to a lower present value?

Higher discount rate

Other things being equal, the more frequent the compounding period, the:

Higher the effective annual interest rate

If $120,000 is borrowed for a home mortgage, to be repaid at 9% interest over 30 years with monthly payments of $965.55, how much interest is paid over the life of the loan?

Interest = (PMT x # of payments) - PV =(965.55*360) - 120000 =$227,598

How much interest will be earned in the next year on an investment paying 12% compounded annually if $100 was just credited to the account for interest?

Interest = Credited Amount * (1+r) 100 x (1+.12) = $112 (investment will pay $100 plus the interest earned)

The opportunity cost of capital:

Is the minimum acceptable rate of return on a project

When will a future value calculated with simple interest exceed a future value calculated with compound interest at the same rate?

It won't. It's not possible with positive interest rates.

When Pat sells her GM common stock at the same time that Brian purchases the same amount of FM stock, GM receives:

Nothing

How much must be invested today in order to generate a 5-year annuity of $1,000 per year, with the first payment 1 year from today, at an interest rate of 12%

PV= $1,000[(1/.12)-(1/(.12*(1.12^5)))] = $3,604.77 (on cheat sheet! Annuity PVAF)

What is the present value of the following set of cash flows at an interest rate of 7%: $1,000 today, $2,000 at the end of year 1, $4,000 at end of year 3, and $6,000 at end of year 5?

PV=FV/(1+r)^n 1. $1,000/(1.07)^0 = $1,000 2. $2,000/(1.07)^1 = $1,869.16 3. $4,000/(1.07)^3 = $3,265.19 4. $6,000/(1.07)^5 = $4,277.92 =$10,412.24

A perpetuity of $5,000 per year beginning today is said to offer a 15% interest rate. What is its present value?

PV=PMT/r = $5,000/.15 =$38,333.33

What is the present value of a 5-period annuity of $3,000 if the interest rate is 12% and the first payment is made today?

PVAF = PMT[(1/r)-(1/r(1+r)^n)] *Because one payment was already made, we drop n from 5 to 4 annual payments, and we'll add the $3,000 for that first payment that had not accumulated interest. =$3,000[(1/.12)-(1/.12(1+.12)^4)]+$3,000 =$12,112.05

$50,000 is borrowed, to be repaid in 3 equal, annual payments with 10% interest. Approximately how much principal is amortized with the first payment?

PVAF = PMT[(1/r)-(1/r(1+r)^n)] Interest for first year: $50,000 * .10 =$5,000 $50,000 = PMT [(1/.1)-(1/.1(1+.1)^3)] = $20,105.74 Principal amortized: $20,105.74-$5,000 =$15,105.74

What will be the monthly payment on a home mortgage of $75,000 at 12% interest to be amortized over 30 years?

PVAF = PMT[(1/r)-(1/r(1+r)^n)] MONTHLY PAYMENTS MEANS DIVIDE R BY 12 AND ENSURE N IS MONTHLY AND NOT YEARLY r = .12/12 = .01 and n = 30 yrs * 12 months = 360 payments $75,000 = PMT [(1/.01)-(1/.01(1+.01)^360)] PMT = $771.46

Your car loan requires payments of $200/month for the first year and payments of $400/month during the second year. The annual interest rate is 12% and payments begin in one month. What is the present value of this 2-year loan?

PVAF = PMT[(1/r)-(1/r(1+r)^n)] Monthly payments: r = .12/12 = .01 n=12 PMT 1 = 200 PMT 2 = 400 (except PVAF equation is divided by 1.01^12) PVAF(1) + PVAF(2) = $6,246.34

What is the present value of a 4-period annuity of $100 per year that begins 2 years from today if the discount rate is 9%?

PVAF = PMT[(1/r)-(1/r(1+r)^n)] PVAF = $100[(1/.09)-(1/.09(1+.09)^4)] =$323.97 --> $323.97/1.09 =$297.22

Approximately how much should be accumulated by the beginning of retirement to provide a $2,500 monthly check that will last for 25 years, during which time the fund will earn 8% interest with monthly compounding?

PVAF = PMT[(1/r)-(1/r(1+r)^n)] r = .08/12 = .00667 n = 300 PVAF = 2500[(1/.00667)-(1/.00667(1+.00667)^300)] =$323,800

Your real estate agent mentions that homes in your price range require a payment of approximately $1,200 per month over 30 years at 9% interest. What is the approximate size of the mortgage with these terms?

PVAF = PMT[(1/r)-(1/r(1+r)^n)] r = .09/12 = .0075 n=360 PVAF = $1,200[(1/.0075)-(1/.0075(1+.0075)^360)] PVAF = $149,138.24

A cash-strapped young professional offers to buy your car with four equal annual payments of $3,000, beginning 2 years from today. Assuming you're indifferent to cash versus credit, that you can invest at 10%, and that you want to receive $9,000 for the car, should you accept?

PVAF=AMT((1/r)-(1/(r(1+r)^n)) =3000(1/.1)-(1/(.1(1.1)^4) =9509.59/1.1 =$8,645 No, the PV is less than what you want to receive

What happens over time to the real cost of purchasing a home if the mortgage payments are fixed in nominal terms and inflation is in existence?

The real cost is decreasing

The salesperson offers, "buy this new car for $25,000 cash or, with appropriate down payment, pay $500/month for 48 months at 8% interest." Assuming that the salesperson does not offer a free lunch, calculate the "appropriate" down payment.

PVAF=PMT[(1/r)-(1/(r(1+r)^n))] where r =r/12 for monthly payments r = .08/12 = .00667 =500[(1/.00667)-(1/(.00667(1+.00667)^48] =$20,479.38 $25,000-$20,479.38 = $4,520.64

How much more is a perpetuity of $1,000 worth than an annuity of the same amount for 20 years? Assume a 10% interest rate and cash flows at the end of period.

Perpetuity: PMT/r Annuity: PMT[(1/r)-(1/(r(1+r)^n))] Perp = $1,000/.1 = $10,000 Annuity = $1,000[(1/.1)-(1/(.1(1.1^20)))] = $8513.56 $10,000-$8,513.56 = $1,486.44

What is the expected real rate of interest for an account that offers a 12% nominal rate of return when the rate of inflation is 6% annually?

Real Interest Rates: 1 + real rate = (1+nominal rate)/(1+inflation) real rate = ((1+.12)/(1+.06)) - 1 =5.66%

Which of the following statements best describes the real interest rate?

Real interest can be negative, zero, or positive.

What is the relationship between an annually compounded rate and the annual percentage rate (APR) which is calculated for truth-in-lending laws for a loan requiring monthly payments?

The APR is lower than the annually compounded rate.

Which of the following characteristics applies to the amortization of a loan such as a home mortgage?

The amortization increases with each payment

Corporate managers are expected to make corporate decisions that are in the best interest of:

The corporations shareholders

An amortizing loan is one in which:

The principal balance is reduce with each payment

How many monthly payments remain to be paid on an 8% mortgage with a 30 year amortization and monthly payments of $733.76 when the balance reaches one-half of the $100,000 mortgage?

Total payments: 30 years x 12 months = 360 payments # of payments to $50,000 = 268 by financial calc or $50,000 = 733.76 x ((1-1.08^-t)/.08) Payments remaining = 360-268 = 92 payments

How may a reduction in cash dividends be in the best interests of current shareholders?

Will have available cash to increase current investment and future portfolios

Which account would be preferred by a depositor: an 8% APR with monthly compounding or 8.5% APR with semiannual compounding?

a) r = .08/12 = .00667 (1+.0067)^12 - 1 = .083 = 8.3% b) r = .085/2 = .0425 (1+.0425)^2 - 1 = .0868 = 8.68% B is preferred

The concept of compound interest refers to:

payment of interest on previously earned interest.

Corporate financing comes ultimately from

savings by households and foreign investors