Tb05 - TB05 PDF

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TB05...

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1.

award:

0.77 points What is the future value of $10,000 on deposit for five years at 6 percent simple interest? $7,472.58 $10,303.62 $13,000.00

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$13,382.26 FV = PV + (PV x r x t) (10,000) + ((10,000 x .06) x 5) = $13,000.00

2.

award:

0.77 points How much will accumulate in an account with an initial deposit of $100, and which earns 10 percent interest compounded quarterly for three years? $107.69 $133.10 $134.49

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$313.84 2

FV = PV (1 + r) 12

100 (1.025)

3.

= 134.49

award:

0.77 points How much can be accumulated for retirement if $2,000 is deposited annually, beginning one year from today, and the account earns 9 percent interest compounded annually for 40 years? $87,200.00

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$675,764.89 $736,583.73 $802,876.27

PV = 2000 = 2000 x 337.8824 = $675,764.89

4.

award:

0.77 points What EAR is being earned on a deposit of $5,000 made ten years ago today if the deposit is worth $9,948.94 today? The deposit pays interest semi-annually. 3.56 percent 6.76 percent

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7.00 percent 7.12 percent

$9,948.94 = $5,000

1.9898 =

1.035 = .035 = 7% = i

5.

award:

0.77 points

Under which of the following conditions will a future value calculated with simple interest exceed a future value calculated with compound interest at the same rate? The interest rate is very high The investment period is very long The compounding is annually This is not possible with positive interest rates

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6.

award:

0.77 points The concept of compound interest refers to: Earning interest on the original investment Payment of interest on previously earned interest

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Investing for a multi-year period of time Determining the APR of the investment

7.

award:

0.77 points When an investment pays only simple interest, this means: The interest rate is lower than on comparable investments The future value of the investment will be low The earned interest is non-taxable to the investor Interest is earned only on the original investment

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8.

award:

0.77 points How much interest is earned in the third year on a $1,000 deposit that earns 7 percent interest compounded annually? $70.00 $80.14

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$105.62 $140.00 2

100 x (1.07) = $1,144.90 after 2 years. $1,144.90 x .07 = $80.14

9.

award:

0.77 points How much interest will be earned in the next year on an investment paying 12 percent compounded annually if $100 was just credited to the account for interest? $88 $100

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$112 $200

The investment will again pay $100 plus interest on the previous interest: $100 x 1.12 = $112.00

10.

award:

0.77 points Assume the total expense for your current year in college equals $20,000. Approximately how much would your parents have needed to invest 21 years ago in an account paying 8 percent compounded annually to cover this amount? $952 $1,600 $1,728

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$3,973 21

$20,000 = x(1.08) $20,000 = 5.0338x $3,973.12 = x

11.

award:

0.77 points

How long must one wait (to the nearest year) for an initial investment of $1,000 to triple in value if the investment earns 8 percent compounded annually? 9

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14 22 25 n

$3,000 = 1,000(1.08) n

3 = (1.08) 14.27, or approx. 14 yrs. = N Solved with financial calculator; can also be solved with tables or logarithms.

12.

award:

0.77 points What will be the approximate population of the United States, if its current population of 275 million grows at a compound rate of 2 percent annually for 25 years? 413 million 430 million

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451 million 466 million 25

275 million x (1.02)

13.

= 451.17 million ≈ 451 million

award:

0.77 points An interest rate that has been annualized using compound interest is termed the: simple interest rate Annual percentage rate Discounted interest rate

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14.

Effective annual interest rate

award:

0.77 points A credit card account that charges interest at the rate of 1.25 percent per month would have an annually compounded rate of _______ and an APR of _______.

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16.08 percent; 15.00 percent 14.55 percent; 16.08 percent 12.68 percent; 15.00 percent 15.00 percent; 14.55 percent 12

Annually compounded rate = (1.0125) -1 = 16.08% APR = 1.25% x 12 = 15.0%

15.

award:

0.77 points In most cases it will save money for consumers to select their loans based on the lowest: Annual percentage rate

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Effective annual rate Number of compounding periods per year Simple interest rate

16.

award:

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

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The APR is lower than the annually compounded rate The APR is higher than the annually compounded rate The APR equals the annually compounded rate The answer depends on the interest rate

17.

award:

0.77 points

What is the APR on a loan that charges interest at the rate of 1.4 percent per month? 10.20 percent 14.00 percent

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16.80 percent 18.16 percent

1.4% monthly X 12 = 16.8% APR

18.

award:

0.77 points How much interest can be accumulated during one year on a $1,000 deposit paying continuously compounded interest at an APR of 10 percent? $100.00

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$105.17 $110.50 $115.70 1

Interest = $1,000 x e. - $1,000 = $1,000 x 1.1052 - $1,000 = $1,105.17 - $1,000 = $105.17

19.

award:

0.77 points If interest is paid m times per year, then the per-period interest rate equals the: Effective annual rate divided by m Compound interest rate times m Effective annual rate

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20.

Annual percentage rate divided by m

award:

0.77 points If the effective annual rate of interest is known to be 16.08 percent on a debt that has quarterly payments, what is the annual percentage rate? 4.02 percent 10.02 percent 14.50 percent

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15.19 percent

25

(1.1608). = 1 + quarterly rate 1.0380 - 1 = quarterly rate .0380 = quarterly rate .1519 = quarterly rate x 4

21.

award:

0.77 points Which account would be preferred by a depositor: an 8 percent APR with monthly compounding or 8.5 percent APR with semi-annual compounding? 8 percent with monthly compounding

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8.5 percent with semi-annual compounding The depositor would be indifferent The time period must be known to select the preferred account

12

(1.0667) -1 = 8.3% 2 (1.0425) -1 = 8.68% Therefore, 'B' is preferred.

22.

award:

0.77 points What is the annually compounded rate of interest on an account with an APR of 10 percent and monthly compounding? 10.00 percent

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10.47 percent 10.52 percent 11.05 percent

(1.00833)

23.

12

-1 = 10.47%

award:

0.77 points What is the APR on a loan with an effective annual rate of 15.01 percent and weekly compounding of interest? 12.00 percent 12.50 percent 13.00 percent

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14.00 percent

1.1501 = 1.0027 = 14% = APR

24.

award:

0.77 points What is the effective annual interest rate on a 9 percent APR automobile loan that has monthly payments? 9.00 percent

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9.38 percent 9.81 percent 10.94 percent 12

Effective rate = (1 + (.09 + 12)) -1 12 = (1.0075) -1 = 1.0938-1 = 9.38%

25.

award:

0.77 points Other things being equal, the more frequent the compounding period, the: Higher the APR Lower the APR

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Higher the effective annual interest rate Lower the effective annual interest rate

26.

award:

0.77 points How much interest will be earned in an account into which $1,000 is deposited for one year with continuous compounding at a 13 percent rate? $130.00

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$138.83 $169.00 $353.34

13

1000 (e. ) = 1000 x 1.1388 = $1,138.83 Thus, $138. 83 was earned in interest.

27.

award:

0.77 points What is the present value of $100 to be deposited today into an account paying 8.0 percent, compounded semi-annually for two years? $85.48

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$100.00 $116.00 $116.99 0

$100 x (1.0375) = $100

28.

award:points 0.77

If a borrower promises to pay you $1,900 nine years from now in return for a loan of $1,000 today, what effective annual interest rate is being offered? 5.26 percent

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7.39 percent 9.00 percent 10.00 percent

PV =

1,000 = 9

(1 + i) = 1.9 1.0739 = 1 + i 7.39% = i

29.

award:

0.77 points th

What is the present value of your trust fund if it promises to pay you $50,000 on your 30 birthday (7 years from today) and earns 10 percent compounded annually? $25,000.00

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$25,657.91 $28,223.70 $29,411.76

PV = = = $25,657.91

30.

award:

0.77 points What is the discount factor for $1 to be received in 5 years at a discount rate of 8 percent? .4693 .5500 .6000

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.6806 5

Discount factor = 1/ (1.08) = 1/1.4693 = .6806

31.

award:

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

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$544.47 $681.48 $740.74 $800.00

PV = Vs. PV =

;

$7,350.30 vs. $6,805.83 $544.47 difference

32.

award:

0.77 points "Give me $5,000 today and I'll return $20,000 to you in five years," offers the investment broker. To the nearest percent, what annual interest rate is being offered? 25 percent

29 percent 32 percent

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60 percent

$5,000 = 5

$5,000 (1+ i) = 20,000 5

(1+ i) = 4 (1+ i ) = 1.3195 i = 31. 95%

33.

award:

0.77 points In calculating the present value of $1,000 to be received 5 years from today, the discount factor has been calculated to be 7008. What is the apparent interest rate? 5.43 percent

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7.37 percent 8.00 percent 9.50 percent

discount factor =

.7008 = 7.37% = i

34.

award:

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

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Higher discount rate Fewer time periods Less frequent discounting Lower discount factor

35.

award:

0.77 points An APR will be equal to an effective annual rate if: Simple interest is used Compounding occurs continuously

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Compounding occurs annually An error has occurred; these terms cannot be equal

36.

award:

0.77 points Cash flows occurring in different periods should not be compared unless: Interest rates are expected to be stable The flows occur no more than one year from each other High rates of interest can be earned on the flows

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37.

The flows have been discounted to a common date

award:

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

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$5,022.11 $5,144.03 $5,423.87 $5,520.00

PV = = 925.93 + 1,714.68 + 2,381.50 = $5,022.11

38.

award:

0.77 points The present value of the following cash flows is known to be $6,939.91; $500 today, $2,000 in one year, and $5,000 in two years. What discount rate is being used? 3 percent 4 percent

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5 percent 6 percent 0

1

2

$6,939.91 = $500/(1 + i) + $2,000/(1 + i) + $5,000/(1 + i) i = 5% by financial calculator

39.

award:

0.77 points What is the present value of the following set of cash flows at an interest rate of 7 percent; $1,000 today, $2,000 at end of year one, $4,000 at end of year three, and $6,000 at end of year five? $9,731

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$10,412 $10,524 $11,524 0

1

3

PV = $1,000/(1.07) + $2,000/(1.07) = $4,000/(1.07) + $6,000/(1.07) = $1,000 + 1,869.16 + 3,265.19 + 4,277.92 = $10,412.27

40.

5

award:

0.77 points A cash-strapped young professional offers to buy your car with four, equal annual payments of $3,000, beginning two years from today. Assuming you're indifferent to cash versus credit, that you can invest at 10 percent, and that you want to receive $9,000 for the car, should you accept? Yes; present value is $9,510 Yes; present value is $11,372

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No; present value is $8,645 No; present value is $7,461 4

PV = $3,000 [1/.1-1/(.1 (1.1) )]/1.1 = $3,000 [10-6.8301]/1.1 = $3,000 [3.1699]/1.1 = $9,509.60/1.1 = $8,645.09

41.

award:

0.77 points How much more is a perpetuity of $1,000 worth than an annuity of the same amount for 20 years? Assume a 10 percent interest rate and cash flows at end of period. $297.29

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$1,486.44 $1,635.08 $2,000.00 20

Difference= $1,000/.10 - $1,000[1/.10-1/.10(1.10) ] = $10,000 - $8,513.56 = $1,486.44

42.

award:

0.77 points A stream of equal cash payments lasting forever is termed: An annuity An annuity due An installment plan

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A perpetuity

43.

award:

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

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Cash payment of a perpetuity Interest rate on a perpetuity Discount rate of a perpetuity

44.

award:

0.77 points The present value of a perpetuity can be determined by: Multiplying the payment by the interest rate Dividing the interest rate by the payment Multiplying the payment by the number of payments to be made

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45.

Dividing the payment by the interest rate

award:

0.77 points A perpetuity of $5,000 per year beginning today is said to offer a 15 percent interest rate. What is its present value? $33,333.33 $37,681.16

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$38,333.33 $65,217.39

PV = $5,000 + = $5,000 + $33,333.33 = $38,333.33

46.

award:

0.77 points What is the present value of a four-period annuity of $100 per year that begins two years from today if the discount rate is 9 percent?

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$297.21 $323.86 $356.85 $388.97

PV1 = 100 = 100 [11.111-7.8714] PV1 = 323.97 PV0 = = $297.21

47.

award:

0.77 points How much must be invested today in order to generate a five-year annuity of $1,000 per year, with the first payment one year from today, at an interest rate of 12 percent?

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$3,604,78 $3,746.25 $4,037.35 $4,604.78

PV = = 3,604.78

48.

award:points 0.77

$50,000 is borrowed, to be repaid in three equal, annual payments with 10% interest. Approximately how much principal is amortized with the first payment? $201.06 $500.00

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$1,510.57 $2,010.57

49.

award:

0.77 points A car dealer offers payments of $522.59 per month for 48 months on an $25,000 car after making a $4,000 down payment. What is the loan's APR? 6 percent

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9 percent 11 percent 12 percent

21,000 = 522.59

40.1848 = r = .0075; or 9% annualized rate

50.

award:

0.77 points A corporation has promised to pay $1,000 twenty years from today for each bond sold now. No interest will be paid on the bonds during the twenty years, and the bonds are said to offer a 7 percent interest rate. Approximately how much should an investor pay for each bond? $70.00

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$258.42 $629.56 $857.43 20

PV = $1,000/(1.07) = $1,000/3.8697 = $258.42

51.

award:

0.77 points A furniture store is offering free credit on purchases of over $1,000. You observe that a big-screen television can be purchased for nothing down and $4,000 due in one year. The store next door offers an identical television for $3,650 but does not offer credit terms. Which statement below best describes the "free" credit?

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The "free" credit costs about 8.75 percent The "free" credit costs about 9.13 percent The "free" credit costs about 9.59 percent The "free" credit effectively costs zero percent

$350/$4,000 = 8.75%

52.

award:

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

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$6,246.34 $6,389.78 $6,428.57 $6,753.05

PV = $200

= 200 [100.0-88.7449] + 400 = $2,251.02 + $3,995.32

= $6,246.34

53.

award:

0.77 points The salesperson offers, "Buy this new car for $25,000 cash or, with appropriate down payment, pay $500 per month for 48 months at 8 percent interest." Assuming that the salesperson does not offer a free lunch, calculate the "appropriate" down payment. $1,000.00

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$4,520.64 $5,127.24 $8,000.00

PV = $500 = $500 [149.925-108.9663] = $500 [40.9587] = $20,479.36 A difference of $4,520.64 exists between cash price and loan value. This should be the down payment.

54.

award:

0.77 points Which of the following will increase the present value of an annuity, other things equal? Increasing the interest rate

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Decreasing the interest rate Decreasing the number of payments Decreasing the amount of the payment

55.

award:

0.77 points What is the present value of a five period annuity of $3,000 if the interest rate is 12 percent and the first payment is made today? $9,655.65 $10,814.33

→

$12,112.05 $13,200.00

PV = 3,000

+3000

= 3,000 [8.33-5.296) + 3,000 = $12,112.05

56.

award:

0.77 points $3,000 is deposited into an account paying 10 percent annually, to provide three annual withdrawals of $1,206.34 beginning in one year....