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Testbankto accompanyFinancial Markets,Institutions & Money3rdeditionPrepared byDr Frédérique BracoudUniversity of Queensland4. © John Wiley & Sons Australia, Ltd Chapter 5: Financial mathematics The present value of $20 000 to be received in 1 month at a simple interest rate ...

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Testbank to accompany

Financial Markets, Institutions & Money rd 3 edition Prepared by Dr Frédérique Bracoud University of Queensland

© John Wiley & Sons Australia, Ltd 2013

Chapter 5: Financial mathematics

Chapter 5: Financial mathematics True/False Questions 1.

Using cash flows ensures that decisions are based on values that are not obscured by accounting rules or accounting choices. *a. b.

True False

Correct answer: a

2.

Interest is paid to borrowers as a compensation for the use of their money by others. a. *b.

True False

Correct answer: b

3.

Interest is the rent or price charged for the temporary use of someone else’s money. *a. b.

True False

Correct answer: a 4.

The time value of money is the concept that a dollar is worth more the later it is received. a. *b.

True False

Correct answer: b

5.

$10 000 invested at 8% per annum (simple interest) will earn $2400 in interest after 2 years. a. *b.

True False

Correct answer: b

© John Wiley & Sons Australia, Ltd 2013

5.2

Testbank to accompany Financial Markets, Institutions and Money 3e

6.

The present value of $20 000 to be received in 1 month at a simple interest rate of 10% per annum is $19 834.71. *a. b.

True False

Correct answer: a

7.

A commercial bill with a face value of $1 000 000, a current price and yield of $973 333.33 and a current yield of 10%, has 100 days to maturity. *a. b.

True False

Correct answer: a 8.

The discount rate on a commercial bill is always higher than its yield. a. *b.

True False

Correct answer: b

9.

A commercial bill is priced using simple interest. *a. b.

True False

Correct answer: a

10.

The nominal rate of interest equals the effective rate only when interest is compounded annually. *a. b.

True False

Correct answer: a 11.

$1000 invested at 15% compounded semi-annually for 2 years has a future value of $1155.63. a. *b.

True False

Correct answer: b

© John Wiley & Sons Australia, Ltd 2013

5.3

Chapter 5: Financial mathematics

12.

The higher the frequency of compounding the higher the present value of a given amount. a. *b.

True False

Correct answer: b

13.

12% per annum compounded quarterly is equivalent to 12.49% per annum compounded annually. a. *b.

True False

Correct answer: b 14.

An annuity due is an ordinary annuity with an extra payment added on to the back end of a series of cash flows. a. *b.

True False

Correct answer: b 15.

The first cash flow of a deferred annuity occurs after several periods have elapsed. *a. b.

True False

Correct answer: a

16.

The present value of a perpetuity is the periodic cash flow divided by the discount rate. *a. b.

True False

Correct answer: a 17.

The yield of a $100 perpetuity paying $10 per annum is 10%. *a. b.

True False

Correct answer: a

© John Wiley & Sons Australia, Ltd 2013

5.4

Testbank to accompany Financial Markets, Institutions and Money 3e

18.

An annuity due is an annuity for which the first payment is deferred for a period greater than the subsequent even-length periods between payments. a. *b.

True False

Correct answer: b

19.

A financial instrument that provides an income stream of unequal amounts is an annuity. a. *b.

True False

Correct answer: b 20.

Bonds can be assimilated to annuities for the part of their income that consists in regular payment of coupons. *a. b.

True False

Correct answer: a

© John Wiley & Sons Australia, Ltd 2013

5.5

Chapter 5: Financial mathematics

Multiple Choice Questions 21.

Which of the following statements is NOT correct? a. Interest compensates lenders for the use of their money. b. Interest is a penalty for borrowers for wanting to consume before earning income. *c. Interest is set by the operator of the financial market in which the financial instrument is issued. d. Interest is set by the supply and demand for funds.

Correct answer: c Learning Objective 5.1 ~ discuss cash flows, interest and the time value of money. 22.

The time value of money is the concept that a dollar is worth a. b. c. *d.

more the later it is received. more the later it is paid. less the sooner it is received. more the sooner it is received.

Correct answer: d Learning Objective 5.1 ~ discuss cash flows, interest and the time value of money. Feedback: A dollar is worth more the sooner it is received because it can bring interest for a longer period.

23.

According to the concept of time value of money, a dollar is worth more the sooner it is received because *a. b. c. d.

it can earn a return. it loses purchase power with time. it can be destroyed with time. the probability to be alive decreases with time.

Correct answer: a Learning Objective 5.1 ~ discuss cash flows, interest and the time value of money.

© John Wiley & Sons Australia, Ltd 2013

5.6

Testbank to accompany Financial Markets, Institutions and Money 3e

24.

If I borrow $20 000 at a simple interest rate of 6% per annum, how much interest would I owe after six months? a. *b. c. d.

$1 200 $600 $21 200 $20 600

Correct answer: b Learning Objective 5.2 ~ solve simple interest problems. Feedback: An interest rate of 6% pa is equivalent to 3% over six months. $20 000 x 0.03 = $600.

25.

Which of the following financial instruments does NOT apply simple interest? a. b. c. *d.

Saving account Term deposit Loan between relatives Annuity

Correct answer: d Learning Objective 5.2 ~ solve simple interest problems.

26.

Simple interest means that a. *b. c. d.

the interest is paid only once. the interest is calculated with respect to the original amount lent. the interest is paid at the beginning of the loan. the interest is calculated with respect to the original amount lent plus the interest already paid.

Correct answer: b Learning Objective 5.2 ~ solve simple interest problems.

© John Wiley & Sons Australia, Ltd 2013

5.7

Chapter 5: Financial mathematics

27.

How much funds will I receive from issuing in Australia a 90 day commercial bill of $50 000 at a yield of 6.6% (assuming no fees)? *a. b. c. d.

$49 199.33 $50 800.67 $49 188.39 $49 186.30

Correct answer: a Learning Objective 5.3 ~ compute the prices of discount securities. Feedback: PV = $50 000/(1 + 0.066  90/365) = $49 199.33. Note that b) cannot be correct, because it is higher than the face value of the bill. c) assumes a 360 day year like in the US. d) applies 6.6% as a discount rather than as a yield.

28.

A 90-day bank bill with a face value of $10 000 and a current price of $9818.43 is trading at a yield of a. b. c. *d.

0.46% 1.85% 7.36% 7.50%

Correct answer: d Learning Objective 5.3 ~ compute the prices of discount securities. Feedback: a) has wrongly inverted the number of days and 365. b) is calculated for 90 days not for the year. c) is the discount rate.

29.

If I receive $49 199.33 from issuing a 90 day commercial bill of $50 000, what was its discount rate (assuming no fees)? a. *b. c. d.

6.51% 6.49% 1.63% 1.60%

Correct answer: b Learning Objective 5.3 ~ compute the prices of discount securities. Feedback: [$50 000 − $49 199.33)/$50 000]  365/90 = 6.49%.

© John Wiley & Sons Australia, Ltd 2013

5.8

Testbank to accompany Financial Markets, Institutions and Money 3e

30.

At the redemption date of a commercial bill the borrower pays a. b. *c. d.

the face value plus interest the face value minus discount the face value the face value plus discount

Correct answer: c Learning Objective 5.3 ~ compute the prices of discount securities.

31.

How much funds will I receive from issuing in Australia a 180 day commercial bill of $70 000 at a yield of 7.2% (assuming no fees)? a. b. *c. d.

$67 567.75 $72 800.67 $67 599.75 $67 514.52

Correct answer: c Learning Objective 5.3 ~ compute the prices of discount securities. 32.

A yield percentage on a commercial bill is _________ the discount rate. a. *b. c. d.

smaller than larger than the same as often smaller and sometimes larger than

Correct answer: b Learning Objective 5.3 ~ compute the prices of discount securities.

© John Wiley & Sons Australia, Ltd 2013

5.9

Chapter 5: Financial mathematics

33.

If I borrow $20 000 at an interest rate of 9% per annum, compounded monthly and payable quarterly how much interest would I have to pay after three months? a. b. *c. d.

$450.00 $150.00 $453.38 $1800.00

Correct answer: c Learning Objective 5.4 ~ understand the compound interest formula so that you can calculate both future and present values. Feedback: Interest expense after one month would be $20 000  0.75% = $150.00. Interest expense after two months would be $150 + $20 150  0.75% = $301.125. Interest expense after three months would be $301.125 + $20 301.125  0.75% = $453.38. Alternatively, one can calculate the future value of $20 000 after three months, compounding at the rate of 0.75% per month and deduct the original amount. FV= $20 000  (1.0075)3 = $20 453.38. Therefore the interest must be $20 453.38 − $20 000 = $453.38.

34.

If you invest $20 000 today for five years at 8% pa compounded quarterly how much will you have at the end of five years? a. b. *c. d.

$28 000 $22 081.62 $29 718.95 $29 680.55

Correct answer: c Learning Objective 5.4 ~ understand the compound interest formula so that you can calculate both future and present values. Feedback: $20,000  (1.02)20 = $29,718.95. 35.

What is the present value of $10 000 to be received in 5 years if the annual discount rate is 10% and compounding frequency is annual? a. $5000.00 b. $16105.10 c. $6666.67 *d. $6209.21

Correct answer: d Learning Objective 5.4 ~ understand the compound interest formula so that you can calculate both future and present values. Feedback: $10,000/(1.1)5 = $6,209.21.

© John Wiley & Sons Australia, Ltd 2013

5.10

Testbank to accompany Financial Markets, Institutions and Money 3e

36.

If the nominal rate of interest is 6% per annum compounded monthly, what is the effective annual rate? a. b. *c. d.

7.20% 6.60% 6.17% 6.00%

Correct answer: c Learning Objective 5.4 ~ understand the compound interest formula so that you can calculate both future and present values. Feedback: (1.005)12 − 1 = 6.17%.

37.

If my bank manager offers me an overdraft at 9% per annum charged quarterly, the effective rate of interest is a. *b. c. d.

9.00% 9.31% 9.38% 9.27%.

Correct answer: b Learning Objective 5.4 ~ understand the compound interest formula so that you can calculate both future and present values. Feedback: (1+0.09/4)4− 1 =(1.0225)4 − 1 = 9.31%. a) is calculated for annual compounding; d) is calculated for the compounding frequency of 3 times per year.

38.

When using the effective rate in calculations, *a. b. c. d.

we need to apply annual compounding. we need to know the actual compounding frequency. we get an approximation of the actual value. we get a different result compared to calculations made with the nominal rate and the actual compounding frequency.

Correct answer: a Learning Objective 5.4 ~ understand the compound interest formula so that you can calculate both future and present values.

© John Wiley & Sons Australia, Ltd 2013

5.11

Chapter 5: Financial mathematics

39.

If I invest $100 per month for two years at 6% per annum compounded monthly, how much will I have after four years? a. b. c. *d.

$2543.20 $5409.78 $2777.54 $2866.59

Correct answer: d Learning Objective 5.4 ~ understand the compound interest formula so that you can calculate both future and present values. Feedback: $100  {[(1.005)24 − 1]/0.005}  (1.005)24 = $100  25.431955  1.12716 = $2866.59. a) is the future value of the annuity after 2 years. b) is the future value of an annuity where the $100 is invested for 4 years. 40.

You borrow $20 000 to be repaid in a lump sum five years from now. The interest rate is 7.2% per annum (nominal), payable quarterly. How much interest will you pay over the term of the loan? a. b. *c. d.

$4519.82 $8 574.96 $7 200.00 $3 993.09

Correct answer: c Learning Objective 5.4 ~ understand the compound interest formula so that you can calculate both future and present values. Feedback: The interest payment each quarter is $20 000  (7.2%  4) = $360. There are 20 quarters in five years. Total interest paid will be $360  20 = $7200. As we use simple interest, we can directly compute the total interest with the equation Pin = $20 000  0.018  20 = $7200. b) is the case where the interest is paid at the end and compounding is quarterly. 41.

If John borrowed $30 000 from his mother at a rate of 5% per annum compounded quarterly for 5 years, what is the dollar value of the interest on the loan? *a. b. c. d.

$8 461.12 $38 461.12 $7 500 $8 288.45

Correct answer: a Learning Objective 5.4 ~ understand the compound interest formula so that you can calculate both future and present values. Feedback: b) is the future value. c) is the simple interest. d) is annual compounding.

© John Wiley & Sons Australia, Ltd 2013

5.12

Testbank to accompany Financial Markets, Institutions and Money 3e

42.

An interest rate is quoted as 8% per annum compounded quarterly. What is the effective annual rate? a. b. *c. d.

8.00% 8.22% 8.24% 8.34%

Correct answer: c Learning Objective 5.4 ~ understand the compound interest formula so that you can calculate both future and present values. Feedback: b) is calculated 4 months not 3 months per compounding period.

43.

An interest rate is quoted as 8% per annum compounded daily. What is the effective annual rate? *a. b. c. d.

8.33% 8.00% 8.30% 8.28%

Correct answer: a Learning Objective 5.4 ~ understand the compound interest formula so that you can calculate both future and present values.

44.

An effective annual rate of 10.52% is equivalent to *a. b. c. d.

10% compounded daily. 10% compounded weekly. 10% compounded monthly. 10% compounded semi-annually.

Correct answer: a Learning Objective 5.4 ~ understand the compound interest formula so that you can calculate both future and present values.

45.

An effective annual rate of 14.98% is equivalent to a. b. *c. d.

14% compounded daily. 14% compounded weekly. 14% compounded fortnightly. 14% compounded monthly.

Correct answer: c

© John Wiley & Sons Australia, Ltd 2013

5.13

Chapter 5: Financial mathematics

Learning Objective 5.4 ~ understand the compound interest formula so that you can calculate both future and present values. 46. What is the present value of an ordinary annuity of $1000 per month for 20 years discounted at 9% per annum (assuming monthly compounding)? a. *b. c. d.

$9128.55 $111 144.95 $11 111.11 $18 508.02

Correct answer: b Learning Objective 5.5 ~ calculate both present and future values of annuities. Feedback: $1000  {[1 − (1.0075)-12X20]/0.0075} = $1000  111.144954 = $111 144.95. a) is for $1000 per year and a yearly compounding. c) keeps the annual discounting rate without doing the pro-rating. d) does the right pro-rating of the discounting rate but uses number of years instead of number of compounding periods.

47.

What is the present value of an annuity due of $1000 per month for 20 years discounted at 9% per annum (assuming monthly compounding)? *a. b. c. d.

$111 978.54 $111 144.95 $9 950.11 $109 978.54

Correct answer: a Learning Objective 5.5 ~ calculate both present and future values of annuities. Feedback: $1,000  {[1 − (1.0075)−239]/0.0075 + 1} = $1,000  111.9785412 = $111,978.54. b) is for an ordinary annuity. c) is with annual compounding. d) is by subtracting 1 instead of adding 1.

48.

What is the present value of a preference share that is expected to pay a dividend of 12 cents per year in perpetuity if the discount rate is 7.5% per annum? a. *b. c. d.

$1.72 $1.60 $2.72 $0.625

Correct answer: b Learning Objective 5.5 ~ calculate both present and future values of annuities. Feedback: $0.12/0.075 = $1.60. d) has wrongly inverted the numerator and the denominator.

© John Wiley & Sons Australia, Ltd 2013

5.14

Testbank to accompany Financial Markets, Institutions and Money 3e

49.

What is the present value of an ordinary annuity of $200 per month for two years, discounted at 6% per annum? (Assume monthly compounding) a. b. c. *d.

$4 800 $5086.39 $ 4 535.14 $ 4 512.57

Correct answer: d Learning Objective 5.5 ~ calculate both present and future values of annuities. Feedback: $200  {[1 − (1.005)-24]/0.005} = $4512.57. a) is the sum of all payments. b) is the future value of the ordinary annuity. c) is the present value of an annuity due.

50.

What is the future value of an ordinary annuity of $100 per month for two years if the interest rate is 12% per annum compounded monthly? a. b. *c. d.

$2124.34 $212.00 $2697.35 $2394.47

Correct answer: c Learning Objective 5.5 ~ calculate both present and future values of annuities. Feedback: $100  {[(1.01)24 − 1]/0.01} = $100  26.9735 = $2697.35. a) is the PV. b) is $100 a year with yearly compounding.

51.

If I can invest at 6% per annum compounded monthly, how much will I need to invest today in order to provide an allowance of $200 per month for two years to a child commencing at boarding school two years from now? (Assume that the first monthly allowance is paid exactly two years from now.) a. *b. c. d.

$4 512.57 $4 023.51 $4 400.14 $8 516.06

Correct answer: b Learning Objective 5.5 ~ calculate both present and future values of annuities. Feedback: $200  {[1 − (1.005)-24]/0.005} / (1.005)23 = $200  22.56286622/1.121552 = $200  20.117539 = $4023.51. a) is the PV of the annuity 2 years from now. d) is the PV of the annuity with $200 per month for four years.

© John Wiley & Sons Australia, Ltd 2013

5.15

Chapter 5: Financial mathematics

52.

A philanthropist wishes to endow a scholarship of $10 000 per year for...