Deck 5: Interest Rates

Question 1

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

A)6.14%
B)6.17%
C)6.00%
D)6.19%

Answer 1

6.14%

Question 2

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)$29 777
B)$29 740
C)$31 250
D)$29 770

Answer 2

$29 770

Question 3

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

Answer 3

False

Question 4

A bank pays interest monthly with an EAR of 6.17%. What is the periodic interest rate applicable per month?

A)0.50%
B)0.55%
C)0.51%
D)0.49%

Question 5

A bank offers an account with an APR of 5% and an EAR of 5.12%. How does the bank compound interest for this account?

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

Question 6

The APR can never exceed the EAR.

Question 7

What is the present value (PV)of an investment that pays $15 000 every year for three years if the interest rate is 5% APR, compounded quarterly?

A)$45 000
B)$40 700
C)$40 760
D)$38 680

Question 8

An 7% APR with quarterly compounding is closest to which of the following?

A)an EAR of 7.19%
B)an EAR of 7.09%
C)an EAR of 7.00%
D)an EAR of 7.12%

Question 9

What is the effective annual rate (EAR)?

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

Question 10

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 11

Melissa is saving for a car. She deposits a fixed amount every month in a bank account with an EAR of 5.5%. If this account pays interest every month then how much should she save from each monthly wage in order to have $15 000 in the account in three years' time?

A)$348
B)$396
C)$4 620
D)$385

Question 12

When there few people looking to save their money and there is high demand for loans, one would expect interest rates to be high.

Question 13

Which of the following accounts has the highest EAR?

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

Question 14

Which of the following best describes the annual percentage rate?

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

Question 15

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 16

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 $3 500 per month. She can borrow at 5% APR, compounded monthly. Assuming that the oven will be used for five years, should she purchase the oven or should she lease it?

A)Buy, since the present value (PV)of the lease is $5 468 more 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)Lease, since the present value (PV)of the lease is $12 224 less than the cost of the oven.

Question 17

A graphic designer needs a laptop for audio/video editing, and notices that they can elect to pay $2 900 for a Dell XPS laptop, or lease from the manufacturer for monthly payments of $79 each for four years. The designer can borrow at an interest rate of 7% APR compounded monthly. What is the cost of leasing the laptop over buying it outright?

A)Leasing costs $311 more than buying.
B)Leasing costs $892 more than buying.
C)Leasing costs $399 more than buying.
D)Leasing costs $384 more than buying.

Question 18

A house costs $138 000. It is to be paid off in exactly 10 years, with monthly payments of $1 675. What is the APR of this loan?

A)7.52%
B)8.33%
C)8.00%
D)7.80%

Question 19

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

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

Question 20

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)$400 000
B)$365 322
C)$364 309
D)$354 223

Question 21

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

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

Question 22

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 $250 000, or you can lease a truck from the manufacturer for five years for a monthly lease payment of $5 000 (paid at the end of each month). Your firm can borrow at 5% APR with quarterly compounding.
A 12% APR with bi-monthly compounding is equivalent to an EAR of

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

Question 23

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 24

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

Question 25

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 $250 000, or you can lease a truck from the manufacturer for five years for a monthly lease payment of $5 000 (paid at the end of each month). Your firm can borrow at 5% APR with quarterly compounding.
The monthly discount rate that you should use to evaluate the truck lease is closest to:

A)0.487%
B)0.4124%
C)0.4175%
D)0.4149%

Question 26

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

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

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

Question 28

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 $250 000, or you can lease a truck from the manufacturer for five years for a monthly lease payment of $5 000 (paid at the end of each month). Your firm can borrow at 5% APR with quarterly compounding.
An 8.5% APR with monthly compounding is equivalent to an EAR of

A)8.77%.
B)8.47%.
C)8.84%.
D)8.51%.

Question 29

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 $250 000, or you can lease a truck from the manufacturer for five years for a monthly lease payment of $5 000 (paid at the end of each month). Your firm can borrow at 5% APR with quarterly compounding.
The effective annual rate on your firm's borrowings is closest to:

A)5.13%
B)5.09%
C)5.06%
D)5.12%

Question 30

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%

Question 31

The present value (PV)of the lease payments for the delivery truck is closest to:

A)$246 459
B)$265 087
C)$256 087
D)$264 954

Question 32

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

Question 33

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

Question 34

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

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

Question 35

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 36

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

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

Question 37

You are considering purchasing a new car 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)$1 454
B)$467
C)$478
D)$527

Question 38

Which of the following statements is FALSE?

A)The annual percentage rate indicates the amount of interest including the effect of compounding.
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)Because 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 our cash flows.

Question 39

The effective annual rate (EAR)for a savings account with a stated APR of 11% compounded daily is closest to:

A)11.57%
B)11.30%
C)11.63%
D)11.46%

Question 40

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

Question 41

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 $270?

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

Question 42

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

Question 43

A small business refits its store. The builders charge them $125 000, which will be paid back in monthly instalments over three years at 6% APR. The builders will reduce this rate to 5.5% APR if they pay $2 500 up front. By approximately how much will this reduce the monthly loan repayments?

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

Question 44

An investor buys a property for $640 000 with a 25-year mortgage and monthly payments at 8% APR. 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)$72 412
B)$84 825
C)$92 644
D)$63 218

Question 45

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)$1 783.33
B)$1 666.66
C)$1 796.54
D)$1 852.62

Question 46

A home buyer buys a house for $225 000. She pays 20% cash, and takes a fixed-rate mortgage for 10 years at 6.26% APR. If she makes payments at the end of every two weeks, which of the following is closest to each of her payments?

A)$915.08
B)$1 165.07
C)$932.05
D)$937.50

Question 47

Use the information for the question(s)below.
Two years ago, you purchased a new car. You financed your car for 60 months (with payments made at the end of the month)with a loan at 6.1% APR. Your monthly payments are $617.16 and you have just made your 24th monthly payment on your car.
The amount of your original loan is closest to:

A)$31 460
B)$33 000
C)$31 846
D)$33 300

Question 48

A Xerox DocuColor photocopier costing $42 000 is paid off in 60 monthly instalments 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)$26 813
C)$19 645
D)$19 842

Question 49

A pottery factory purchases a continuous belt conveyor kiln for $50 000. A 6.5% APR loan with monthly payments is taken out to purchase the kiln. If the monthly payments are $501, over what term is this loan being paid?

A)13 years
B)10 years
C)12 years
D)11 years

Question 50

A homeowner has five years of monthly payments of $1 400 before she has paid off her house. If the interest rate is 7% APR, what is the remaining balance on her loan?

A)$59 890
B)$84 000
C)$64 918
D)$70 703

Question 51

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 amortising loan.

Question 52

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)$1 086
C)$736
D)$594

Question 53

A $40 000 new car loan is taken out with the terms 9% APR for 48 months. How much are monthly payments on this loan?

A)$833.33
B)$1 002.56
C)$769.79
D)$995.40

Question 54

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 point, you will need to borrow an additional $3 250 to cover the point 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 paying the point? Show your calculations.

Question 55

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

A)$87 255
B)$28 678
C)$31 432
D)$24 867

Question 56

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 $5 000 to cover points you are paying the lender.
Assuming you pay the points and borrow from the mortgage lender at 6.00%, then your monthly mortgage payment (with payments made at the end of the month)will be closest to:

A)$1 570
B)$1 540
C)$1 530
D)$1 500

Question 57

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 $5 000 to cover points you are paying the lender.
Assuming you do not pay the points and borrow from the mortgage lender at 6.25%, then your monthly mortgage payment (with payments made at the end of the month)will be closest to:

A)$1 540
B)$1 500
C)$1 570
D)$1 530

Question 58

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)84 months
C)98 months
D)78 months

Question 59

Use the information for the question(s)below.
Two years ago, you purchased a new car. You financed your car for 60 months (with payments made at the end of the month)with a loan at 6.1% APR. Your monthly payments are $617.16 and you have just made your 24th monthly payment on your car.
Assuming that you have made all of the first 24 payments on time, then the outstanding principal balance on your car loan is closest to:

A)$20 256
B)$20 200
C)$20 250
D)$20 365

Question 60

You are in the process of purchasing a new motorbike 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 a bike 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? Show your calculations.

Question 61

If over the course of a year the inflation rate was about 3.24%, and short-term government bonds offered a rate of 2.9%, which of the following statement is correct?

A)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.
B)The real interest rate for investors in these bonds was greater than the rate of inflation.
C)The nominal interest rate offered by these bonds gave the true increase in purchasing power that resulted from investing in these bonds.
D)The purchasing power of investors in these bonds grew over the course of the year.

Question 62

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

Question 63

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

Question 64

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 total principal paid will decrease 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 mortgage balance will decrease faster with $1 000 monthly payments compared to $900 monthly payments.
D)The total interest expense will increase with $1 000 monthly payments compared to $900 monthly payments.

Question 65

Which of the following formulas gives you the growth in purchasing power?

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

Question 66

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

Question 67

What is the real interest rate given a nominal rate of 8% and an inflation rate of 4.5%?

A)8.0%
B)3.3%
C)4.9%
D)4.5%

Question 68

A homeowner has $200 000 home with a 20-year mortgage, paid monthly at 7.25% 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)3 years
B)5 years
C)6 years
D)4 years

Question 69

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 you save in total interest expense?

A)$75 848
B)$151 696
C)$100 998
D)$176 846

Question 70

Liam had an extension built onto his home. He financed it for 60 months with a loan at 5.1% APR. His monthly payments were $650. How much was the loan amount for this extension?

A)$34 360
B)$34 420
C)$34 000
D)$34 842

Question 71

If interest rates are 4.5% and inflation is 2.8%, what is the real interest rate?

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

Question 72

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

Question 73

Joseph buys a Jeep 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, 9 months
B)4 years, 4 months
C)4 years, 10 months
D)4 years, 6 months

Question 74

Historically, why have high inflation rates tended to be associated with high nominal interest rates?

A)Growth in investment and savings is encouraged when consumers are judged to be overspending.
B)High inflation leads to a decrease in purchasing power and thus increases the attractiveness of investment over consumption in the short term.
C)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.
D)Individuals will spend more when they expect their investments to increase in value.

Question 75

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

Question 76

In which of the following situations would it NOT be appropriate to use the following formula: PV = C₀ + C₁/(1 + r)+ C₂/(1 + r)² + . . . . + C_n/(1 + r)ⁿ
When determining the present value (PV)of a cash flow stream?

A)when yield curves are flat
B)when short-term and long-term interest rates vary widely
C)when the discount rate is high
D)when the inflation rate is high

Question 77

A reserve bank would be most likely to lower interest rates if the economy were growing slowly or not at all.

Question 78

Fundamentally, interest rates are determined by the RBA.

Question 79

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

Question 80

Coby buys 10 Tufflift 4-post, 4.5-tonne car hoists for his car park 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)$250 698
B)$150 969
C)$287 153
D)$302 284