Deck 5: Interest Rates

Question 1

Your bank account pays quarterly interest with an APR of 7%.What is the EAR?

A) 7.50%
B) 7.2%
C) 7.0%
D) 7.8%
E) 8.0%

Answer 1

7.2%

Question 2

Your bank account pays daily interest with an APR of 4.5%.What is the EAR?

A) 4.0%
B) 4.8%
C) 4.5%
D) 4.6%
E) 4.4%

Answer 2

4.6%

Question 3

What is the effective annual rate (EAR)?

A) the interest rate that would earn the same interest with annual compounding
B) the ratio of the number of the annual percentage rate to the number of compounding periods per year
C) the discount rate for an n-year time interval, where n may be more than one year or less than or equal to one year (a fraction)
D) the cash flows from an investment over a one-year period divided by the number of times that interest is compounded during the year
E) the amount of simple interest earned in one year without considering the effects of compounding.

Answer 3

the interest rate that would earn the same interest with annual compounding

Question 4

When you borrow money,the interest rate on the borrowed money is the price you pay to be able to convert your future loan payments into money today.

Question 5

Your bank account pays monthly interest with an APR of 8%.You are planning to buy a house in 6 years,and you wish to save $40,000 for the down payment.If you currently have no money in your account,how much will you need to save at the end of each month?

A) $451.18
B) $500.34
C) $555.56
D) $434.66
E) $438.53

Question 6

Your bank account pays monthly interest with an EAR of 8%.What amount of interest will you earn each month?

A) 0.64%
B) 0.67%
C) 1.00%
D) 0.60%
E) 0.80%

Question 7

Drew receives an inheritance that pays him $50,000 every three months for the next two years.Which of the following is closest to the present value (PV)of this inheritance if the interest rate is 8.5% (EAR)?

A) $354,223
B) $364,309
C) $365,322
D) $400,000
E) $339,782

Question 8

Which of the following best describes the annual percentage rate?

A) the quoted interest rate which considered with the compounding period gives the effective interest rate
B) the effective annual rate after compounding is taken into account
C) the discount rate when compounded more than once a year or less than once a year
D) the discount rate when it is divided by the number of of times it is compounded in a year
E) the total amount of interest that will be earned in one year

Question 9

A bank offers a loan that will requires you to pay 6% interest compounded monthly.Which of the following is closest to the EAR charged by the bank?

A) 5.84%
B) 6.00%
C) 6.17%
D) 72.00%
E) 6.48%

Question 10

Your bank account pays quarterly interest with an EAR of 7%.What amount of interest will you earn each quarter?

A) 1.80%
B) 1.75%
C) 1.70%
D) 1.50%
E) 2.00%

Question 11

A bank offers an account with an APR of 6% and an EAR of 6.09%.How does the bank compound interest for this account?

A) weekly compounding
B) monthly compounding
C) semi-annual compounding
D) annual compounding
E) daily compounding

Question 12

An 8% APR with monthly compounding is closest to which of the following?

A) an EAR of 6.7%
B) an EAR of 7.72%
C) an EAR of 8.3%
D) an EAR of 8.5%
E) an EAR of 9.14%

Question 13

Your bank account pays monthly interest with an EAR of 10%.You are planning to buy a house in 10 years,and you wish to save $100,000 for the down payment.If you currently have no money in your account,how much will you need to save at the end of each month?

A) $833.33
B) $500.35
C) $488.17
D) $9646.39
E) $475.13

Question 14

Which of the following accounts has the highest EAR?

A) one that pays 6.1% every six months
B) one that pays 1.0% per month
C) one that pays 12.6% per year
D) one that pays 3% every three months
E) one that pays 0.2% per week

Question 15

The annual percentage rate indicates the amount of interest,including the effect of any compounding.

Question 16

Howard is saving for a long holiday.He deposits a fixed amount every month in a bank account with an EAR of 7.5%.If this account pays interest every month then how much should he save from each monthly paycheck in order to have $10,000 in the account in two years' time?

A) $161
B) $166
C) $388
D) $4818
E) $417

Question 17

The table above shows the rate of return (APR)for four investment alternatives.Which offers the highest EAR?

A) Investment A
B) Investment B
C) Investment C
D) Investment D
E) Investment E

Question 18

Your bank account pays quarterly interest with an APR of 8.75%.What is the EAR?

A) 9.25%
B) 8.5%
C) 8.4%
D) 8.75%
E) 9.0%

Question 19

Which of the following would be most likely to lower the interest rate that a bank offers a borrower?

A) The number of borrowers seeking funds is high.
B) The expected inflation rate is expected to be high.
C) The borrower is judged to have a low degree of risk.
D) The investment will be for a long period of time.
E) The number of savers depositing funds at the bank is low.

Question 20

When there are large numbers of people looking to save their money and there is little demand for loans,one would expect interest rates to be high.

Question 21

Use the information for the question(s) below.
Two years ago you purchased a new SUV. You financed your SUV for 60 months (with payments made at the end of the month) with a loan at 5.9% APR. You monthly payments are $617.16 and you have just made your 24th monthly payment on your SUV.
Assuming that you have made all of the first 24 payments on time,then the outstanding principal balance on your SUV loan is closest to:

A) $31,250
B) $20,300
C) $19,200
D) $32,000
E) $29,000

Question 22

You are considering purchasing a new truck that will cost you $34,000.The dealer offers you 1.9% APR financing for 48 months (with payments made at the end of the month).Assuming you finance the entire $34,000 and finance through the dealer,your monthly payments will be closest to:

A) $708
B) $594
C) $736
D) $1086
E) $697

Question 23

Use the information for the question(s) below.
Your firm needs to invest in a new delivery truck. The life expectancy of the delivery truck is five years. You can purchase a new delivery truck for an upfront cost of $200,000, or you can lease a truck from the manufacturer for five years for a monthly lease payment of $4000 (paid at the end of each month). Your firm can borrow at 6% APR with quarterly compounding.
The monthly discount rate that you should use to evaluate the truck lease is closest to:

A) 0.487%
B) 0.512%
C) 0.498%
D) 0.500%
E) 0.504%

Question 24

Use the information for the question(s) below.
Two years ago you purchased a new SUV. You financed your SUV for 60 months (with payments made at the end of the month) with a loan at 5.9% APR. You monthly payments are $617.16 and you have just made your 24th monthly payment on your SUV.
The amount of your original loan is closest to:

A) $37,000
B) $32,000
C) $20,300
D) $31,250
E) $29,000

Question 25

A small foundry agrees to pay $250,000 two years from now to a supplier for a given amount of coking coal.The foundry plans to deposit a fixed amount in a bank account every three months,starting three months from now,so that at the end of two years the account holds $250,000.If the account pays 5.5% APR compounded monthly,how much must be deposited every three months?

A) $29,770
B) $29,777
C) $29,740
D) $31,250
E) $28,077

Question 26

Use the table for the question(s) below.
Consider the following investment alternatives:

The highest effective rate of return you could earn on any of these investments is closest to:

A) 6.250%
B) 6.267%
C) 6.300%
D) 6.310%
E) 6.245%

Question 27

Use the table for the question(s) below.
Consider the following investment alternatives:

Which alternative offers you the highest effective rate of return?

A) Investment A
B) Investment B
C) Investment C
D) Investment D
E) Investment E

Question 28

Use the table for the question(s) below.
Consider the following investment alternatives:

The lowest effective rate of return you could earn on any of these investments is closest to:

A) 6.245%
B) 6.267%
C) 6.100%
D) 6.300%
E) 6.250%

Question 29

Emma runs a small factory that needs a vacuum oven for brazing small fittings.She can purchase the model she needs for $180,000 up front,or she can lease it for five years for $4200 per month.She can borrow at 7% APR,compounded monthly.Assuming that the oven will be used for five years,should she purchase the oven or should she lease it?

A) Lease, since the present value (PV) of the lease is $12,224 less than the cost of the oven.
B) Lease, since the present value (PV) of the lease is $8642 less than the cost of the oven.
C) Lease, since the present value (PV) of the lease is $2212 less than the cost of the oven.
D) Buy, since the present value (PV) of the lease is $32,108 more than the cost of the oven.
E) Buy, since the present value (PV) of the lease is $72,000 more than the cost of the oven.

Question 30

Use the information for the question(s) below.
Your firm needs to invest in a new delivery truck. The life expectancy of the delivery truck is five years. You can purchase a new delivery truck for an upfront cost of $200,000, or you can lease a truck from the manufacturer for five years for a monthly lease payment of $4000 (paid at the end of each month). Your firm can borrow at 6% APR with quarterly compounding.
The effective annual rate on your firm's borrowings is closest to:

A) 6.00%
B) 6.24%
C) 6.17%
D) 6.14%
E) 6.18%

Question 31

Use the information for the question(s) below.
Your firm needs to invest in a new delivery truck. The life expectancy of the delivery truck is five years. You can purchase a new delivery truck for an upfront cost of $200,000, or you can lease a truck from the manufacturer for five years for a monthly lease payment of $4000 (paid at the end of each month). Your firm can borrow at 6% APR with quarterly compounding.
The present value (PV)of the lease payments for the delivery truck is closest to:

A) $206,900
B) $207,050
C) $207,680
D) $198,420
E) $205,475

Question 32

Use the information for the question(s) below.
You are purchasing a new home and need to borrow $250,000 from a mortgage lender. The mortgage lender quotes you a rate of 6.25% APR for a 30-year fixed rate mortgage. The mortgage lender also tells you that if you are willing to pay two points, they can offer you a lower rate of 6.0% APR for a 30-year fixed rate mortgage. One point is equal to 1% of the loan value. So if you take the lower rate and pay the points, you will need to borrow an additional $5000 to cover points you are paying the lender.
Assuming you do not pay the points and borrow from the mortgage lender at 6.25%,your monthly mortgage payment (with payments made at the end of the month)will be closest to:

A) $1570
B) $1530
C) $1540
D) $1500
E) $1510

Question 33

You are considering purchasing a new automobile that will cost you $28,000.The dealer offers you 4.9% APR financing for 60 months (with payments made at the end of the month).Assuming you finance the entire $28,000 and finance through the dealer,your monthly payments will be closest to:

A) $1454
B) $527
C) $467
D) $478
E) $497

Question 34

What is the present value (PV)of an investment that pays $10,000 every year for four years if the interest rate is 7% APR,compounded quarterly?

A) $33,730
B) $33,872
C) $38,680
D) $40,000
E) $30,516

Question 35

Use the information for the question(s) below.
Two years ago you purchased a new SUV. You financed your SUV for 60 months (with payments made at the end of the month) with a loan at 5.9% APR. You monthly payments are $617.16 and you have just made your 24th monthly payment on your SUV.
A 12% APR with bi-monthly compounding is equivalent to an EAR of:

A) 11.98%
B) 12.50%
C) 12.00%
D) 12.62%
E) 12.14%

Question 36

The effective annual rate (EAR)for a savings account with a stated APR of 4% compounded daily is closest to:

A) 4.00%
B) 4.10%
C) 4.08%
D) 4.06%
E) 4.05%

Question 37

Use the information for the question(s) below.
You are purchasing a new home and need to borrow $250,000 from a mortgage lender. The mortgage lender quotes you a rate of 6.25% APR for a 30-year fixed rate mortgage. The mortgage lender also tells you that if you are willing to pay two points, they can offer you a lower rate of 6.0% APR for a 30-year fixed rate mortgage. One point is equal to 1% of the loan value. So if you take the lower rate and pay the points, you will need to borrow an additional $5000 to cover points you are paying the lender.
Assuming you pay the points and borrow from the mortgage lender at 6.00%,your monthly mortgage payment (with payments made at the end of the month)will be closest to:

A) $1540
B) $1530
C) $1570
D) $1500
E) $1510

Question 38

Use the table for the question(s) below.
Consider the following investment alternatives:

Which alternative offers you the lowest effective rate of return?

A) Investment A
B) Investment B
C) Investment C
D) Investment D
E) Investment E

Question 39

The effective annual rate (EAR)for a loan with a stated APR of 10% compounded quarterly is closest to:

A) 10.52%
B) 10.25%
C) 10.38%
D) 10.00%
E) 10.47%

Question 40

The effective annual rate (EAR)for a loan with a stated APR of 8% compounded monthly is closest to:

A) 8.30%
B) 8.33%
C) 8.00%
D) 8.24%
E) 8.16%

Question 41

You decide to take out a 25-year mortgage for $375,000 at 5% APR.What will your outstanding balance be at the end of the mortgage's initial 5-year term?

A) $330,000
B) $332,176
C) $331,584
D) $331,903
E) $244,139

Question 42

You decide to take out a car loan at 4.5% APR for 60 months.If your monthly payments are $512.68,what is the price of your car?

A) $30,000
B) $10,581
C) $30,761
D) $32,145
E) $27,500

Question 43

What care,if any,should be taken when cash flows occur in periodicities that are shorter than a year-e.g.,quarterly or monthly cash flows?

Question 44

You are in the process of purchasing a new automobile that will cost you $25,000.The dealership is offering you either a $1000 rebate (applied toward the purchase price)or 3.9% financing for 60 months (with payments made at the end of the month).You have been pre-approved for an auto loan through your local credit union at an interest rate of 7.5% for 60 months.Should you take the $1000 rebate and finance through your credit union or forgo the rebate and finance through the dealership at the lower 3.9% APR?

Question 45

You decide to take out a car loan for $14,995 at 3% APR for 48 months.How much are your monthly payments?

A) $312.40
B) $321.77
C) $331.90
D) $593.47
E) $336.17

Question 46

You decide to take out a 30-year mortgage for $445,000 at 6% APR.What are your monthly payments?

A) $2,622.69
B) $2,646.96
C) $2,694.06
D) $2,688.32
E) $2,667.99

Question 47

You decide to take out a car loan for $34,575 at 4% APR for 72 months.How much are your monthly payments?

A) $480.21
B) $540.93
C) $1,470.30
D) $549.63
E) $499.42

Question 48

You decide to take out a 25-year mortgage for $350,000 at 5% APR.What are your monthly payments?

A) $2,035.62
B) $2,046.07
C) $1,166.67
D) $2,069.45
E) $2,054.11

Question 49

Joe borrows $100,000 and agrees to repay the principal,plus 7% APR interest compounded monthly,at the end of three years.Joe has taken out an amortizing loan.

Question 50

Everything else remaining the same,under what situation will APR and EAR be equal?

Question 51

Which of the following is/are TRUE? I.The EAR can never exceed the APR.
II)The APR can never exceed the EAR.
III)The APR and EAR can never be equal.

A) Only I is true.
B) Only II is true.
C) Only II & III are true.
D) Only I & III are true.
E) Only III is true.

Question 52

You decide to take out a car loan for $25,000 at 6% APR for 60 months.What is the outstanding principal of your loan after you make your first payment?

A) $24,875.00
B) $24,516.68
C) $24,641.68
D) $24.734.32
E) $24,975.14

Question 53

A $60,000 loan is taken out on a boat with the terms 7% APR for 36 months.How much are the monthly payments on this loan?

A) $1666.66
B) $1783.33
C) $1796.54
D) $1852.62
E) $1901.24

Question 54

Is it possible to analyze cash flows that occur in time intervals that are not exactly equal to a year?

Question 55

You decide to take out a car loan for $20,000 at 7% APR for 60 months.How much are your monthly payments?

A) $396.02
B) $333.33
C) $406.48
D) $400.00
E) $367.54

Question 56

Ursula wants to buy an $18,999 used car.She has savings of $2,000 plus an $800 trade-in.She wants her monthly payments to be about $272.Which of the following loans offers monthly payments closest to $272?

A) 6.5% APR for 36 months
B) 6.5% APR for 48 months
C) 6.5% APR for 60 months
D) 6.5% APR for 72 months
E) 6.5% APR for 84 months

Question 57

You decide to take out a car loan for $35,000 at 5% APR with monthly payments of $838.12.Over how many years is your loan being paid?

A) 2 years
B) 3 years
C) 4 years
D) 5 years
E) 6 years

Question 58

What is the general relationship between the absolute values of APR and EAR for an investment?

Question 59

You are purchasing a new home and need to borrow $325,000 from a mortgage lender.The mortgage lender quotes you a rate of 6.5% APR for a 30-year fixed rate mortgage (with payments made at the end of each month).The mortgage lender also tells you that if you are willing to pay one point,they can offer you a lower rate of 6.25% APR for a 30-year fixed rate mortgage.One point is equal to 1% of the loan value.So if you take the lower rate and pay the points,you will need to borrow an additional $3250 to cover points you are paying the lender.Assuming that you do not intend to prepay your mortgage (pay off your mortgage early),are you better off paying the one point and borrowing at 6.25% APR or just taking out the loan at 6.5% without any points?

Question 60

How do we handle a situation when both compounding period and cash flow interval are given to us,but both are less than a year and not equal to each other?

Question 61

Michael has credit card debt of $60,000 that has an 18% APR,compounded monthly.The minimum monthly payment only requires him to pay the interest on his debt.He receives an offer for a credit card with an APR of 10% compounded monthly.If he rolls over his debt onto this card and makes the same monthly payment as before,how long will it take him to pay off his credit card debt?

A) 72 months
B) 78 months
C) 84 months
D) 98 months
E) 104 months

Question 62

Liam had an extension built onto his home.He financed it for 48 months with a loan at 4.9% APR.His monthly payments were $750.How much was the loan amount for this extension?

A) $32,631
B) $34,842
C) $36,000
D) $38,420
E) $37,764

Question 63

A construction company takes a loan of $280,000 to cover the cost of a new grader.If the interest rate is 8.75%APR,and payments are made monthly for five years,what percentage of the outstanding principal does the company pay in interest each month?

A) 0.73%
B) 7.29%
C) 8.75%
D) 9.25%
E) 10.5%

Question 64

How are interest and return of principal handled in an amortizing loan payment?

Question 65

Five years ago you took out a 30-year mortgage with a quoted APR of 6.5% for $200,000.If you were to refinance the mortgage today for 20 years at a quoted APR of 4.25% ,how much would you save in total interest expense?

A) $176,846
B) $75,848
C) $151,696
D) $98,770
E) $108,340

Question 66

Five years ago you took out a 30-year mortgage with a quoted APR of 6.5% for $200,000.If you were to refinance the mortgage today for 20 years at a quoted APR of 4.25%,,by how much would your monthly payment change?

A) The monthly payment will increase by $98.33.
B) The monthly payment will decrease by $98.33.
C) The monthly payment will increase by $343.12.
D) The monthly payment will decrease by $343.12.
E) The monthly payment will not change.

Question 67

A house costs $138,000.It is to be paid off in exactly ten years,with monthly payments of $1675.What is the quoted APR of this mortgage?

A) 7.52%
B) 7.80%
C) 8.14%
D) 8.33%
E) 8.54%

Question 68

An investor buys a property for $640,000 with a 25-year mortgage and monthly payments at a quoted APR of 8%.After 18 months the investor resells the property for $712,000.How much cash will the investor have made from the sale,once the mortgage is paid off?

A) $63,218
B) $72,412
C) $85,082
D) $92,644
E) $72,000

Question 69

What is a mortgage?

Question 70

Corey buys 10 Tufflift 4-post,4.5-ton car hoists for his parking garage at a total cost of $410,000.He finances this with a five-year loan at 6.2% APR with monthly payments.After he has made the first 20 payments,how much is the outstanding principal balance on his loan?

A) $150,969
B) $250,698
C) $287,153
D) $302,284
E) $310,104

Question 71

Assume your current mortgage payment is $900 per month.If you begin to pay $1,000 per month (with the extra $100 per month going to principal),which of the following will be TRUE?

A) The mortgage balance will decrease faster with $1,000 monthly payments compared to $900 monthly payments.
B) The total paid (principal and interest) will increase with $1,000 monthly payments compared to $900 monthly payments.
C) The total interest expense will increase with $1,000 monthly payments compared to $900 monthly payments.
D) The total principal paid will decrease with $1,000 monthly payments compared to $900 monthly payments.
E) The time until your mortgage is paid off will increase with $1,000 monthly payments compared to $900 monthly payments

Question 72

A homeowner has a $200,000 home with a 20-year mortgage,paid monthly at a quoted APR of 7.25%.After five years he receives $50,000 as an inheritance.If he pays this $50,000 toward his mortgage along with his regular payment,by approximately how many years will it reduce the amount of time it takes him to pay off his mortgage?

A) 6 years
B) 5 years
C) 4 years
D) 3 years
E) 2 years

Question 73

A small business refits its store.The builders charge them $125,000,which will be paid back in monthly installments over three years at 6% APR.The builders will reduce this rate to 5.5% APR if they pay $2500 up front.By approximately how much will this reduce the monthly loan repayments ?

A) $104
B) $28
C) $214
D) $77
E) $192

Question 74

A home buyer buys a house for $225,000.She pays 20% cash,and takes a fixed-rate mortgage for ten years at a quoted APR of 6.26%.If she makes biweekly payments,which of the following is closest to each of her payments?

A) $915.08
B) $928.61
C) $937.50
D) $1165.07
E) $1160.76

Question 75

Market forces determine interest rates based ultimately on the willingness of individuals,banks,and firms to borrow,save,and lend.

Question 76

A truck costing $112,000 is paid off in monthly installments over four years with 8% APR.After three years the owner wishes to sell the truck.What is the closest amount from the following list that he needs to pay on his loan before he can sell the truck?

A) $24,867
B) $28,678
C) $31,432
D) $87,255
E) $44,792

Question 77

A homeowner has five years of monthly payments of $1400 before she has paid off her house.If the quoted interest rate is 7% APR,what is the remaining balance on her mortgage?

A) $59,890
B) $64,918
C) $70,872
D) $84,000
E) $88,830

Question 78

Joseph buys a Hummer for $60,000,financing it with a five-year 6.5% APR loan paid monthly.He decides to pay an extra $50 per month in addition to his monthly payments.Approximately how long will he take to pay off the loan under these conditions?

A) 4 years 10 months
B) 4 years 9 months
C) 4 years 6 months
D) 4 years 4 months
E) 5 years

Question 79

The real interest rate is the rate of growth of one's purchasing power due to money invested.

Question 80

A Xerox DocuColor photocopier costing $42,000 is paid off in 60 monthly installments at 6.5% APR.After three years the company wishes to sell the photocopier.What is the minimum price for which they can sell the copier so that they can cover the cost of the balance remaining on the loan?

A) $18,448
B) $19,645
C) $19,842
D) $26,813
E) $17,946