Deck 5: Interest Rates

Question 1

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.

Answer 1

False

Question 2

A bank offers an account with an APR of 5.8% and an EAR of 5.88%. How does the bank compound interest for this account?

A) weekly compounding
B) monthly compounding
C) semiannual compounding
D) annual compounding

Answer 2

semiannual compounding

Question 3

The effective annual rate (EAR) for a savings account with a stated APR of 5% compounded daily is closest to ________.

A) 5.64%
B) 6.15%
C) 5.13%
D) 6.66%

Answer 3

5.13%

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

A bank pays interest semiannually with an EAR of 13%. What is the periodic interest rate applicable semiannually?

A) 5.04%
B) 7.56%
C) 6.30%
D) 12.60%

Question 6

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 effective annual rate is divided by the number of times it is compounded in a year

Question 7

A bank offers a loan that will requires you to pay 7% interest compounded monthly. Which of the following is closest to the EAR charged by the bank?

A) 5.78%
B) 8.68%
C) 7.23%
D) 14.46%

Question 8

What is the effective annual rate (EAR)?

A) It is the interest rate that would earn the same interest with annual compounding.
B) It is the ratio of the number of the annual percentage rate to the number of compounding periods per year.
C) It is the interest 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) It refers to the cash flows from an investment over a one-year period divided by the number of times that interest is compounded during the year.

Question 9

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

A) The number of borrowers seeking funds is low.
B) The expected inflation rate is expected to be low.
C) The borrower is judged to have a low degree of risk.
D) The loan will be for a long period of time.

Question 10

Howard is saving for a holiday. He deposits a fixed amount every month in a bank account with an EAR of 14.7%. If this account pays interest every month then how much should he save from each monthly paycheck in order to have $14,000 in the account in four years' time?

A) $176
B) $308
C) $220
D) $352

Question 11

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

Question 12

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

A) 8.30%
B) 9.13%
C) 9.96%
D) 10.79%

Question 13

An animator needs a laptop for audio/video editing, and notices that he can pay $2600 for a Dell XPS laptop, or lease from the manufacturer for monthly payments of $75 each for four years. The designer can borrow at an interest rate of 14% APR compounded monthly. What is the cost of leasing the laptop over buying it outright?

A) Leasing costs $116 more than buying.
B) Leasing costs $174 more than buying.
C) Leasing costs $145 more than buying.
D) Leasing costs $289 more than buying.

Question 14

A(n) 12% APR with monthly compounding is closest to ________.

A) an EAR of 10.14%
B) an EAR of 15.22%
C) an EAR of 12.68%
D) an EAR of 25.36%

Question 15

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

Question 16

The effective annual rate (EAR) for a loan with a stated APR of 11% compounded quarterly is closest to ________.

A) 12.61%
B) 13.75%
C) 11.46%
D) 14.90%

Question 17

Drew receives an inheritance that pays him $54,000 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 8.9% (EAR)?

A) $314,366
B) $471,549
C) $392,957
D) $432,000

Question 18

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

Question 19

Which of the following accounts has the highest EAR?

A) one that pays 5.4% every six months
B) one that pays 1.0% per month
C) one that pays 9.6% per year
D) one that pays 2.4% every three months

Question 20

Which of the following statements is FALSE about interest rates?

A) As interest rates may be quoted for different time intervals, it is often necessary to adjust the interest rate to a time period that matches that of cash flows.
B) The effective annual rate indicates the amount of interest that will be earned at the end of one year.
C) The annual percentage rate indicates the amount of simple interest earned in one year.
D) The annual percentage rate indicates the amount of interest including the effect of compounding.

Question 21

A pottery factory purchases a continuous belt conveyor kiln for $68,000. A 6.3% APR loan with monthly payments is taken out to purchase the kiln. If the monthly payments are $765.22, over what term is this loan being paid?

A) 8 years
B) 9 years
C) 10 years
D) 11 years

Question 22

A $50,000 new car loan is taken out with the terms 12% APR for 48 months. How much are monthly payments on this loan?

A) $1448.36
B) $1580.03
C) $1316.69
D) $1711.70

Question 23

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 24

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

Question 25

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

Question 26

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

Question 27

Which of the following is/are TRUE? I. The EAR can never exceed the APR.

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

Question 28

A 10% APR with quarterly compounding is equivalent to an EAR of ________.

A) 10.00%
B) 10.47%
C) 10.38%
D) 9.81%

Question 29

Consider the following investment alternatives: The lowest effective rate of return you could earn on any of these investments is closest to ________.

A) 6.3830%
B) 6.4080%
C) 6.4330%
D) 6.4580%

Question 30

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 31

A $52,000 loan is taken out on a boat with the terms 3% APR for 36 months. How much are the monthly payments on this loan?

A) $1663.45
B) $1814.67
C) $1965.89
D) $1512.22

Question 32

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 $300,000, or you can lease a truck from the manufacturer for five years for a monthly lease payment of $6000 (paid at the end of each month). Your firm can borrow at 8.00% APR with quarterly compounding. The monthly discount rate that you should use to evaluate the truck lease is closest to ________.

A) 0.5298%
B) 0.7947%
C) 0.6623%
D) 0.6667%

Question 33

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

Question 34

Ursula wants to buy a $19,000 used car. She has savings of $2,000 plus an $800 trade-in. She wants her monthly payments to be about $282. Which of the following loans offers monthly payments closest to $282?

A) 7.8% APR for 36 months
B) 7.8% APR for 48 months
C) 7.8% APR for 60 months
D) 7.8% APR for 72 months

Question 35

Consider the following investment alternatives: The highest effective rate of return you could earn on any of these investments is closest to ________.

A) 6.0860%
B) 6.1110%
C) 6.1610%
D) 6.1360%

Question 36

A 12% APR with bimonthly compounding is equivalent to an EAR of ________.

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

Question 37

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 $350,000, or you can lease a truck from the manufacturer for five years for a monthly lease payment of $7000 (paid at the end of each month). Your firm can borrow at 9.00% APR with quarterly compounding. The effective annual rate on your firm's borrowings is closest to ________.

A) 9.00%
B) 7.45%
C) 11.17%
D) 9.31%

Question 38

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 39

When computing a present value, which of the following is TRUE?

A) You should adjust the discount rate to match the interval between cash flows.
B) You should adjust the future value to match the present value.
C) You should adjust the time period to match the present value.
D) You should adjust the cash flows to match the time period of the discount rate.

Question 40

A house costs $148,000. It is to be paid off in exactly ten years, with monthly payments of $1737.54. What is the APR of this loan?

A) 6.25%
B) 5.25%
C) 7.25%
D) 8.25%

Question 41

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 $4,200 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 $8,642 less than the cost of the oven.
C) Lease, since the present value (PV) of the lease is $2,212 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.

Question 42

A truck costing $111,000 is paid off in monthly installments over four years with 8.10% 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) $24,956
B) $37,434
C) $31,195
D) $43,673

Question 43

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 payment compared to $900 monthly payments.
B) The total amount paid (principal and interest) will increase with $1,000 monthly payment compared to $900 monthly payments.
C) The total interest expense will increase with $1,000 monthly payment compared to $900 monthly payments.
D) The total principal paid will decrease with $1,000 monthly payment compared to $900 monthly payments.

Question 44

A home buyer buys a house for $2,155,000. She pays 20% cash, and takes a fixed-rate mortgage for ten years at 7.70% APR. If she makes semi-monthly payments, which of the following is closest to each of her payment?

A) $11,342.47
B) $10,311.34
C) $12,373.61
D) $8249.07

Question 45

Corey buys 10 Tufflift 4-post, 4.5-ton car hoists for his parking garage at a total cost of $432,000. He finances this with a five-year loan at 7.80% APR with monthly payments. After he has made the first 20 payments, how much is the outstanding principal balance on his loan?

A) $244,965
B) $428,689
C) $306,206
D) $612,412

Question 46

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

A) The monthly payment will increase by $104.79.
B) The monthly payment will decrease by $104.79
C) The monthly payment will increase by $343.12.
D) The monthly payment will decrease by $343.12.

Question 47

Five years ago you took out a 30-year mortgage with an APR of 6.20% for $206,000. If you were to refinance the mortgage today for 20 years at an APR of 3.95%, how much would you save in total interest expense?

A) $200,503
B) $150,377
C) $50,126
D) $100,251

Question 48

Michael has a credit card debt of $60,000 that has a 10% 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 9% 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) 298 months
B) 299 months
C) 306 months
D) 308 months

Question 49

An investor buys a property for $608,000 with a 25-year mortgage and monthly payments at 8.10% APR. After 18 months the investor resells the property for $667,525. How much cash will the investor have from the sale, once the mortgage is paid off?

A) $57,216
B) $100,129
C) $71,521
D) $143,041

Question 50

Joseph buys a Hummer for $59,000, financing it with a five-year 7.60% 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) 59.57 months
B) 57.07 months
C) 54.57 months
D) 60.57 months

Question 51

A homeowner has five years of monthly payments of $1400 before she has paid off her house. If the interest rate is 6% APR, what is the remaining balance on her loan?

A) $57,933
B) $86,899
C) $72,416
D) $101,382

Question 52

What is the present value (PV) of an investment that pays $100,000 every year for four years if the interest rate is 5% APR, compounded quarterly?

A) $353,818
B) $389,200
C) $424,581
D) $459,963

Question 53

A homeowner has a $227,000 home with a 20-year mortgage, paid monthly at 6.60% APR. 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) 5.5 years
B) 8.6 years
C) 10.2 years
D) 12.8 years

Question 54

You are considering purchasing a new automobile with the upfront cost of $25,000 or leasing it from the dealer for a period of 60 months. The dealer offers you 4.00% APR financing for 60 months (with payments made at the end of the month). Assuming you finance the entire $25,000 through the dealer, your monthly payments will be closest to ________.

A) $368
B) $460
C) $552
D) $645

Question 55

A Xerox DocuColor photocopier costing $44,000 is paid off in 60 monthly installments at 6.90% 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) $19,433
B) $15,546
C) $23,319
D) $27,206

Question 56

A small business repairs its store. The builders charge them $130,000 which will be paid back in monthly installments over three years at 6.80% APR. The builders will reduce this rate to 6.30% APR if they pay $2600 up front. By approximately how much will this reduce the monthly loan repayments?

A) $109
B) $218
C) $164
D) $55

Question 57

A construction company takes a loan of $1,531,000 to cover the cost of a new grader. If the interest rate is 6.75% APR, and payments are made monthly for five years, what percentage of the outstanding principal does the company pay in interest each month?

A) 0.56%
B) 5.63%
C) 0.51%
D) 0.61%
E) 0.66%

Question 58

Liam had an extension built onto his home. He financed it for 48 months with a loan at 5.00% APR. His monthly payments were $770. How much was the loan amount for this extension?

A) $33,436
B) $40,123
C) $46,810
D) $53,497

Question 59

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 $240,000, or you can lease a truck from the manufacturer for five years for a monthly lease payment of $4800 (paid at the end of each month). Your firm can borrow at 7.80% APR with quarterly compounding. The present value (PV) of the lease payments for the delivery truck is closest to ________.

A) $190,506
B) $238,132
C) $285,758
D) $333,385

Question 60

A small foundry agrees to pay $220,000 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 $220,000. If the account pays 12.5% APR compounded monthly, how much must be deposited every three months?

A) $24,602
B) $27,063
C) $29,523
D) $31,983

Question 61

Given that the inflation rate in 2006 was about 3.24%, while a short-term municipal bond offered a rate of 2.9%, which of the following statements is correct?

A) The purchasing power of investors in these bonds grew over the course of the year.
B) The real interest rate for investors in these bonds was greater than the rate of inflation.
C) Investors in these bonds were able to buy less at the end of the year than they could have purchased at the start of the year.
D) The nominal interest rate offered by these bonds gave the true increase in purchasing power that resulted from investing in these bonds.

Question 62

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 5.95% APR. Your monthly payments are $386.19 and you have just made your 24th monthly payment on your SUV. The amount of your original loan is closest to ________.

A) $22,000
B) $20,000
C) $24,000
D) $28,000

Question 63

You are considering purchasing a new automobile with the upfront cost of $26,000 or leasing it from the dealer for a period of 48 months. The dealer offers you 2.80% APR financing for 48 months (with payments made at the end of the month). Assuming you finance the entire $26,000 through the dealer, your monthly payments will be closest to ________.

A) $459
B) $688
C) $573
D) $802

Question 64

When the costs of an investment come before that investment's benefits, what will be the effect of a rise in interest rates on the attractiveness of that investment to potential investors?

A) It will make it more attractive, since it will increase the investment's net present value (NPV).
B) It will make it more attractive, since it will decrease the investment's net present value (NPV).
C) It will make it less attractive, since it will increase the investment's net present value (NPV).
D) It will make it less attractive, since it will decrease the investment's net present value (NPV).

Question 65

Historically, why were high inflation rates associated with high nominal interest rates?

A) Individuals will spend more when they expect their investments to increase in value.
B) Growth in investment and savings is encouraged when consumers are judged to be overspending.
C) High inflation leads to a decrease in purchasing power and thus increases the attractiveness of investment over consumption in the short term.
D) The real interest rate needs to be high enough so that individuals can expect their savings to have greater purchasing power in the future than in the present.

Question 66

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

Question 67

Which of the following computes the growth in purchasing power?

A) growth of money + growth of prices
B) (1 + real rate) / (1 + nominal rate)
C) (1 + inflation rate) / (1 + nominal rate)
D) growth of money / growth of prices

Question 68

Quality adjustments to changes in the CPI most often result in reductions to the inflation rate calculated from it.

Question 69

In 2007, interest rates were about 4.5% and inflation was about 2.8%. What was the real interest rate in 2007?

A) 1.58%
B) 1.61%
C) 1.62%
D) 1.65%

Question 70

What is the real interest rate given a nominal rate of 8.9% and an inflation rate of 1.9%?

A) 6.9%
B) 8.2%
C) 9.6%
D) 11.0%

Question 71

You are purchasing a new home and need to borrow $260,000 from a mortgage lender. The mortgage lender quotes you a rate of 6.80% 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 6.50% 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 $5200 to cover points you are paying the lender. Assuming you pay the points and borrow from the mortgage lender at 6.50%, then your monthly mortgage payment (with payments made at the end of the month) will be closest to ________.

A) $1844
B) $1676
C) $2011
D) $2347

Question 72

You are purchasing a new home and need to borrow $380,000 from a mortgage lender. The mortgage lender quotes you a rate of 5.75% 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 5.45% 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 $7600 to cover points you are paying the lender. Assuming you do not pay the points and borrow from the mortgage lender at 5.75%, then your monthly mortgage payment (with payments made at the end of the month) will be closest to ________.

A) $2439
B) $2661
C) $2218
D) $3105

Question 73

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 $3,250 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 74

You are in the process of purchasing a new automobile that will cost you $25,000. The dealership is offering you either a $1,000 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 $1,000 rebate and finance through your credit union or forgo the rebate and finance through the dealership at the lower 3.9% APR?

Question 75

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 6.15% APR. Your monthly payments are $388.05 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) $14,000
B) $12,727
C) $15,273
D) $17,818

Question 76

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

Question 77

The table above shows the interest rates available from investing in risk-free U.S. Treasury securities with different investment terms. If an investment offers a risk-free cash flow of $100,000 in two years' time, what is the present value (PV) of that cash flow?

A) $76,518
B) $114,777
C) $133,906
D) $95,647

Question 78

Which of the following situations would result in lowering of interest rates by the banking authority of a country?

A) The economy is slowing down.
B) Inflation is rising rapidly.
C) The level of investment is quite high.
D) The rate of savings is quite low.

Question 79

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

Question 80

The table above shows the interest rates available from investing in risk-free U.S. Treasury securities with different investment terms. What is the present value (PV) of cash flows from an investment that yields $6000 at the end of each year for the next four years?

A) $18,111
B) $27,167
C) $31,695
D) $22,639