FIN3400 Ch. 5 Smartbook

Which statement correctly applies to this monthly loan payment calculation? PMT360 = $145,000 × {0.005/[1 - 1/(1 + 0.005)^(360)]} = $869.35

The APR is 6 percent. Rationale: 0.005 × 12 = 0.06 = 6%

What is the future value in year 7 of these cash flows: Year 0 = $200; Year 1 = $240; Year 3 = $300; and Year 4 = $400? The interest rate is 6 percent.

$1,496.32 Rationale: FV7 = ($200 × 1.067) + ($240 × 1.066) + ($300 × 1.064) + ($400 × 1.063) = $1,496.32

A 6 percent, $11,500 car loan requires monthly payments. What rate should be used in the calculator input to determine the number of periods until the loan is repaid in full?

0.5 percent Rationale: The annual rate is 6 percent. Since the loan payments are monthly, the rate per period is 1/12th of 6 percent, or 0.5 percent.

what is the effective annual rate of a 6 percent APR compounded daily?

6.18 percent

Rusty Industries has decided to save $50,000 a year for two years and then increase that amount to $80,000 for an additional three years. Which one of these formulas will correctly compute the future value of these savings as of Year 5 at a rate of 7 percent?

FVA5 = [$50,000 × (1.07^5 - 1)/0.07] + [$30,000 × (1.07^3 - 1)/0.07]

Which one of these correctly converts an ordinary future value annuity formula into an annuity due future value formula?

FVAN due = FVAN × (1 + i)

You expect to receive $800 next year, $400 three years from now, and $500 four years from now. Which one of these formulas will correctly compute the present value as of today at 5 percent interest?

PV = $800/1.05 + $400/1.05^3 + $500/1.05^4

which one of these correctly summarizes the future value formula? assume the interest rate is positive.

the greater the number of time period, the higher the future value, all else held constant.

A 3-year investment pays 5 percent annual interest with semiannual interest payments. How is the EAR computed?

EAR = [1 + (0.05/2)]^(2) - 1 Rationale: When raising fractions to a power, you must add and then subtract one. EAR = [1 + (0.05/2)]2 - 1.

You just borrowed money for four years to buy a car. The payments are $218 a month and the APR is 7 percent. How is the EAR computed?

EAR = [1 + (0.07/12)^(12) - 1]

Bro is buying $35,000 to buy a new car; how much can are his interest payments if the rate is 3.5% over three years?

$1,025.57 Rationale: You need to compute the present value, not the future value. N = 36; I = 3.5/12; PV = $35,000; FV = 0; CPT PMT

You expect to receive annual gifts of $1,000 at the end of Years 1 and 2 and $1,500 at the end of Years 3 and 4. Which of these is the correct present value of multiple annuities formula if the rate is 6 percent?

$1,500 × {[1 - (1/1.06^4)]/0.06} - $500 × {[1 - (1/1.06^2)]/0.06}

Alex expects to incur personal costs of $3,800 in Year 1, and $4,300, $5,200 and $4,600 in costs over the following three years, respectively. What is the present value of these costs at 7 percent.

$15,061.26 Rationale: PV = $3,800/1.07 + $4,300/1.072 + $5,200/1.073 + $4,600/1.074 = $15,061.26

A 12-month add-on interest loan has monthly payments of $220 and an interest rate of 5 percent. How do you compute the amount borrowed?

Amount borrowed = (12 × $220)/(1 + 0.05) Rationale: Total principal including interest = 12 × $220; Amount borrowed = (12 × $220)/(1 + 0.05)

Identify a true statement about the effective annual rate.

An effective annual rate is higher than annual percentage rate if compounding of interest happens more than once in a year.

Chris plans on saving $4,000 a year at 4 percent interest for five years. Which one of these is the correct formula for computing the future value at Year 5 of these savings? Assume the payments occur at the end of each year.

FV5 = $4,000 × [(1.04^5 -1)/0.04]

which one of these illustrates a perpetuity?

payments of $50 a quarter from now until forever

Les sold some equipment and will receive annual payments of $400 for two years and $350 for the following two years. Which is the correct present value of multiple annuities formula given a rate of 9 percent?

$350 × {[1 - (1/1.09^4)]/0.09} + $50 × {[1 - (1/1.09^2)]/0.09}

You want to gift $1,000 every year forever and earn 5 percent on your investments. How much must you invest to accomplish this goal?

$20,000 Rationale: PV = $1,000/0.05 = $20,000

How do you convert an ordinary annuity present value formula to an annuity due present value formula?

Multiply the ordinary annuity present value by (1 + i) Rationale: Multiply the ordinary annuity present value by (1 + i) to get the annuity due present value.

Justine pays $200 a month for five years at 6 percent interest. Which of these is the correct input for determining the amount borrowed?

N = 60; I = 6/12; PMT = -200; FV = 0; CPT PV

What is an amortization schedule?

An amortization schedule shows the interest and principal portions of each payment, as well as the loan balance after each payment.

You have decided to save $500 a year for the next five years and then increase that amount to $700 a year for the following five years. Which one of these correctly reflects a multiple annuity time line for the future value of your savings?

The time line will have a -$500 cash flow for Years 1 - 10 and an additional -$200 cash flow for Years 6 - 10. Rationale: Using multiple annuities, the -$500 cash flow will be for Years 1 - 10 with an additional -$200 cash flow for Years 6 - 10.

true or false: a cash outflow three years from now will appear as a positive value at year 3 on a present value time line. Assume today is Time 0.

false

You have decided to invest for 20 years. You start with $200 a year and plan to increase that amount every three years by an additional $100 a year with the first increase occurring in Year 4. You create a multiple annuity future value time line. What cash flows will appear at Year 7 on the annuity time line?

Year 7 will have three cash flows in the amounts of -$200, -$100, and -$100.

You want to compute the future value of a 20-year ordinary annuity that pays 7 percent interest. Which one of these correctly represents the annuity compounding factor that should be used in the FVAN equation?

[(1.07)^(20) - 1]/0.07

An annuity pays a rate of 8 percent and has a life of 12 years. Which of these is the correct annuity discount factor for computing a present value of this annuity?

[1 - (1/1.08^12)]/0.08

Reiss has invested $5,000 at the end of every year for the past 22 years and earns 8 percent annually. If he continues doing this, how much will his investment account be worth 12 years from now?

$793,133 Rationale: Using a financial calculator: N = 34; I = 8; PV = 0; PMT = -5,000; CPT FV; FV = $793,133 FVA8 = $5,000 × {[(1 + 0.08)34 - 1]/0.08} = $793,133

You are comparing four loans with the following rates. Which loan offers the best interest rate for the borrower?

5% APR, compounded annually Rationale: The EAR equals the APR since compounding is annual.

You are comparing four loans with the following rates. Which loan offers the best interest rate for the borrower?

6.15 percent APR, compounded annually Rationale: The EAR equals the APR since compounding is annual.

Assume the answers provided are the effective annual rates with annual, semiannual, quarterly, and monthly compounding of the identical APR. Which rate must be the monthly EAR? (No computations are required.)

7.576 Rationale: This is the rate given semiannual compounding. The more frequent the compounding, the higher the EAR.

How is an ordinary annuity defined?

An ordinary annuity is a stream of equal cash flows paid at the end of every time period.

An annuity due sees payments at the [BLANK 1] of each period while an annuity assumes payments at the [BLANK 2] of each period.

Blank 1: beginning or start Blank 2: end

Which one of these sets of cash flows fits the description of an ordinary annuity?

Car payments of $240 a month for four years with the first payment due one month after the loan is obtained

You borrow money for two years at 1.25 percent per month. How is the effective annual rate (EAR) computed?

EAR = (1 + 0.0125)^(12) - 1

An investment pays quarterly payments and has an APR of 8 percent. You need to compute the future value at Year 3. What is the calculator input for the interest rate?

I = 8/4 Rationale: Since there are four quarters per year, the annual rate should be divided by four.

Tory invested $600 a year for three years, then $700 a year for an additional four years. In year 9, she withdrew $1,500. She withdrew the entire investment in year 11. Which statement correctly applies to the time line for this problem?

The cash flows for the first seven years are negative. Rationale: Withdrawals are cash inflows (positive values) and investments are cash outflows (negative values). The cash flows are negative for the first seven years, but the amount in year 4 is $700, not $600. While there are only nine cash flows, there are 12 time periods, including time 0. Time periods 0, 8, and 10 have no cash flows.

Lester's rented some equipment at a cost of $800 for Years 1 through 3 and $900 for Years 4 and 5. Which of these correctly depicts a portion of the present value of multiple annuities time line?

Year 1 has two cash flows in the amounts of -$900 and $100.

You just signed a contract and will receive $500 at the end of the next two years and $800 at the end of each of the following three years. At 4 percent, what is this contract worth today?

$2,995.63 Rationale: PVA0 = $800 × {[1 - (1/1.045)]/0.04} - $300 × {[1 - (1/1.042)]/0.04 = $2,995.63

Which one of these loans meets the definition of an add-on interest loan?

Leo borrowed $1,000 at 10 percent for one year. The initial principal loan balance was computed as $1,000 + $100 = $1,100. Rationale: $1,000 + (0.10 × $1,000) = $1,100

Art's Market borrows $25,000 for three years at 8 percent. Payments are quarterly. Which of these inputs correctly computes the payment amount?

N = 12; I = 8/4; PV = 25,000; FV = 0; CPT PMT

Which one of these illustrates a perpetuity?

Preferred stock which pays a $60 annual dividend Rationale: A perpetuity pays equal payments that never end. This illustrates an annuity. A perpetuity has unending payments. This illustrates an annuity. A perpetuity has unending payments.

Which one of these statements is correct regarding the present value of multiple cash flows formula? Assume a positive interest rate.

The higher the interest rate, the lower the present value, all else held constant.

You borrow $500 at 10 percent for one year. The loan is an add-on interest loan. Which one of these provides the correct calculation to determine the monthly payment?

[$500 + (0.10 × $500)]/12

what is the difference between annuity and a perpetuity?

an annuity has a fixed number of cash flows while perpetuity has unending cash flows.

how is an effective annual rate defined?

an effective annual rate is the rate per year which includes interest rate compunding

How many times do you discount a cash flow received immediately?

0

You just incurred a loan with annual payments of $1,200 at 6 percent for five years. How much did you borrow? (Do not round intermediate calculations.)

$5,054.84 Rationale: PVA5 = $1,200 × {[1 - (1/1.065)]/0.06} = $5,054.84

What is a perpetuity?

A perpetuity is an unending stream of equal payments occurring at equal intervals of time.

Which one of these payment streams fits the definition of an annuity due?

A prize pays $1,000 a year for ten years, starting today.

You take out a $120,000 mortgage for 30 years at 4 percent interest. The monthly payment is $572.90. How much of your second payment applies to the principal balance?

$173.48 Rationale: First payment: Interest = $400, Principal = $172.90; Second payment: Interest = $399.42, Principal = $173.48

Stu deposited $400 in an account three years ago. Last year, he deposited $250 and plans to deposit $300 next year. The rate is 3 percent. Which one of these correctly states a portion of the formula needed to compute the future value five years from today?

$250 × 1.03^6 Rationale: The deposit was made one year ago and the FV is 5 years from now, thus, the exponent is 6.

You endow a chair in Finance for your favorite finance professor. He will earn $150,000 every year forever and you believe you can earn 5% on your investments. How much must you invest to accomplish this goal?

$3,000,000 Rationale: PV = $150,000/0.05 = $3,000,000

An investment will pay $400 a year for 25 years. What is the correct formula to compute the present value of these payments at a rate of 5 percent?

$400 × {[1 - (1/1.05^(25))]/0.05}

How many times per year is interest compounded on a debt that requires monthly payments?

12 times Rationale: There are 12 months in a year, so compounding occurs 12 times.

You pay $366.09 a month on your mortgage. The interest rate is 5 percent and the remaining principal balance is $9,656.21. How long will it be until your mortgage is paid off?

28 months Rationale: Since the payments are monthly, the problem is solved in months. I/Y = 5/12; PV = 9,656.21; PMT = -366.09; FV = 0; CPT N; N = 28, which is the number of months.

Which one of these is the definition of an amortized loan?

An amortized loan is a loan in which the borrower pays interest and principal over time.

True or false: To calculate the future value of multiple annuities, simply compute the future value of each one separately and add them together.

True Rationale: Each annuity is calculated separately as there is no cross compounding.

True or false: Time has a greater impact on a future value than the interest rate.

True Rationale: Time is the exponential factor and thus time has a greater impact on the future value than the interest rate.

you expect to receive $600 in years 1 through 5, $700 in years 6 through 8, and $400 in years 9 and 10. What cash flow(s) will appear on a present value of multiple annuities time line for year 10?

year 10 has one cash inflow in the amount of $400

Which one of these loans meets the definition of an amortized loan?

A loan requires quarterly payments of $500. The loan will be repaid in full when the last $500 payment is paid.

You expect to receive the following annual cash flows starting at Year 1: $800, $500, $900, and $600. To develop a time line, what will the cash flow for Year 3 be?

+$900

A $24,000 loan has an interest rate of 9.5 percent and quarterly payments of $936.05. How many years will it take to repay this loan?

10 years Rationale: Since the payments are quarterly, the problem is solved in quarters. I/Y = 9.5/4; PV = 24,000; PMT = -936.05; FV = 0; CPT N; N = 40 quarters = 10 years

Two years ago, Margo deposited $500 into a savings account. One year ago, she deposited an additional $300, and today she deposited $800. Which one of these is these is the correct formula for computing the value of these deposits today at a rate of 4 percent?

FV2 = ($500 × 1.042) + ($300 × 1.04) + $800

You can afford monthly car payments of $150 for five years at 7 percent. How do you compute the amount you can borrow?

N = 60; I = 7/12; PMT = -150; FV = 0; CPT PV

A credit card charges an interest rate of one percent per month. Define the annual percentage rate (APR) for this debt.

The APR is equal to one percent per month multiplied by 12 months per year.

True or false: The lower the interest rate, the lower the present value of a set of multiple future cash flows, all else held constant.

False Rationale: The lower the interest rate, the higher the present value. If you earn less interest, you need more money today to obtain the same future values.

You sell some equipment for $8,000 and agree to accept annual payments of $2,469.35 for four years. If you draw a time line, what is the cash flow for Year 4?

+$2,469.35 Rationale: Since you are the lender in this case, the payments are cash inflows.

You borrow $18,000 for four years to buy a car. The APR is 8 percent. What rate should be used when you compute the monthly payment?

0.67 percent Rationale: The annual rate is 8 percent. The monthly rate is computed by dividing the annual rate by 12.

You plan to invest $300 today and $500 three years from today. Two years from today, you plan to withdraw $50. Which of these is a correct statement regarding a time line for computing the future value of your cash flows four years from today?

The cash flow at year 3 is a negative $500.

A loan charges an APR of 11 percent with payments made quarterly. How is the EAR computed?

EAR = [1 + (0.11/4)]^(4) - 1

You just won a prize that will pay you $800 today and $500 a year for the next three years. Which is the correct formula for computing the present value as of today at 6 percent?

PV = $800 + $500/1.06 + $500/1.06^2+ $500/1.06^3

You take out a $120,000 mortgage for 30 years at 4% interest. How much of your first payment applies to the principal balance?

$172.90 Rationale: First payment: Interest = $400, Principal = $172.90; Second payment: Interest = $399.42, Principal = $173.48

You just bough a home with annual payments of $12,000 at 4% for 30 years. How much did you borrow? (Do not round intermediate calculations.)

$207,504 Rationale: PVA5 = $1,200 × {[1 - (1/1.065)]/0.06} = $5,054.84

You wish to retire with an annuity that will pay you $30,000 for the next 25 years and then $50,000 at the end of the 26th year. At 5%, what is this contract worth today?

$436,880 Rationale: PVA0 = $50,000 × {[1 - (1/1.05^26)]/0.05} - $20,000 × {[1 - (1/1.05^25)]/0.05}

Sis can afford monthly car payments of $180 for three years. How much can she borrow if the rate is 7 percent?

$5,829.56 Rationale: You need to compute the present value, not the future value. N = 36; I = 7/12; PMT = -180; FV = 0; CPT PV

Domenic will invest $12,000 at the end of every year for the next 50 years and earns 9.9% annually. How much will his investment account be worth 45 years from now?

$6,966,411 Rationale: Using a financial calculator: N = 45; I = 9.9; PV = 0; PMT = -10,000; CPT FV; FV = $6,966,411

What is the future value in year 7 of these cash flows: Year 0 = $200; Year 1 = -$100; Year 3 = $200; and Year 4 = $200? The interest rate is 10%.

$771.61 Rationale: FV7 = ($200 × 1.067) - ($100 × 1.066) + ($200 × 1.064) + ($200 × 1.063) = $771.31

You borrow $10,000 for four years to buy a car. The monthly loan payment is $237.15. If you draw a time line, what is the cash flow at Time 0?

+$10,000 Rationale: The amount borrowed is a cash inflow so it should be a positive value.

how is the annual percentage rate (APR) defined?

an APR is the interest rate per period times the number of periods per year.

What is the table called which lists the amount of each loan payment, the interest and principal portions of each payment, and the remaining principal balance?

Amortization schedule

Which one of these best defines an annuity due?

An annuity due is a stream of equal payments paid at the beginning of each equal time interval for a set number of time periods.

What is the difference between an annuity and a perpetuity?

An annuity has a fixed number of cash flows while a perpetuity has unending cash flows.

Which one of these payment streams is an annuity due?

An auto lease calls for monthly payments of $250 with the first payment due at lease signing.

You borrowed $16,000 at 8 percent with semiannual payments of $707.23. What is the correct calculator input to compute the time period?

I = 8/2; PV = 16,000; PMT = -707.23; FV = 0; CPT N, which is the number of semiannual periods

an investment pays an annual rate of 9 percent with interest payments occurring quarterly. how many times per year is the interest compounded?

4 times

Which type of loan computes the amount of interest at the beginning of the loan by applying the interest rate to the amount borrowed and includes that interest in the loan principal?

Add-on interest loan

You borrow money for two years at 1.25 percent per month. How is the effective annual rate (EAR) computed?

EAR = (1 + 0.0125)^(12) - 1 Rationale: The rate given is a rate PER month, which means the 1.25 percent is a monthly, not an annual rate. EAR = (1 + 0.0125)12 - 1.

Which one of these formulas correctly defines an effective annual rate (EAR) for any compounding period?

EAR = (1 + Rate per period)Number of periods per year - 1.