# Quiz 5: Financial Mathematics

Business

Q 1Q 1

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

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True False

True

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True False

False

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True False

True

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True False

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True False

Q 6Q 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.

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True False

Q 7Q 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.

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True False

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True False

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True False

Q 10Q 10

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

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True False

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True False

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True False

Q 13Q 13

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

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True False

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True False

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True False

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True False

Q 17Q 17

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.

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True False

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True False

Q 19Q 19

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.

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Multiple Choice

Q 20Q 20

The time value of money is the concept that a dollar is worth:
A)more the later it is received.
B)more the later it is paid.
C)less the sooner it is received.
D)more the sooner it is received.

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Multiple Choice

Q 21Q 21

According to the concept of time value of money,a dollar is worth more the sooner it is received because:
A)it can earn a return.
B)it loses purchase power with time.
C)it can be destroyed with time.
D)the probability to be alive decreases with time.

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Multiple Choice

Q 22Q 22

If I borrow $20 000 at a simple interest rate of 6% per annum,how much interest would I owe after six months?
A)$1 200
B)$600
C)$21 200
D)$20 600

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Multiple Choice

Q 23Q 23

Which of the following financial instruments does NOT apply simple interest?
A)Saving account
B)Term deposit
C)Loan between relatives
D)Annuity

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Multiple Choice

Q 24Q 24

Simple interest means that:
A)the interest is paid only once.
B)the interest is calculated with respect to the original amount lent.
C)the interest is paid at the beginning of the loan.
D)the interest is calculated with respect to the original amount lent plus the interest already paid.

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Multiple Choice

Q 25Q 25

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)$49 199.33
B)$50 800.67
C)$49 188.39
D)$49 186.30

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Multiple Choice

Q 26Q 26

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)0.46%
B)1.85%
C)7.36%
D)7.50%

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Multiple Choice

Q 27Q 27

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)6.51%
B)6.49%
C)1.63%
D)1.60%

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Multiple Choice

Q 28Q 28

At the redemption date of a commercial bill the borrower pays:
A)the face value plus interest
B)the face value minus discount
C)the face value
D)the face value plus discount

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Multiple Choice

Q 29Q 29

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)$67 567.75
B)$72 800.67
C)$67 599.75
D)$67 514.52

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Multiple Choice

Q 30Q 30

A yield percentage on a commercial bill is _________ the discount rate.
A)smaller than
B)larger than
C)the same as
D)often smaller and sometimes larger than

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Multiple Choice

Q 31Q 31

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)$450.00
B)$150.00
C)$453.38
D)$1800.00

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Multiple Choice

Q 32Q 32

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)$28 000.00
B)$22 081.62
C)$29 718.95
D)$29 680.55

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Multiple Choice

Q 33Q 33

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

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Multiple Choice

Q 34Q 34

If the nominal rate of interest is 6% per annum compounded monthly,what is the effective annual rate?
A)7.20%
B)6.60%
C)6.17%
D)6.00%

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Multiple Choice

Q 35Q 35

If my bank manager offers me an overdraft at 9% per annum charged quarterly,the effective rate of interest is:
A)9.00%
B)9.31%
C)9.38%
D)9.27%.

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Multiple Choice

Q 36Q 36

When using the effective rate in calculations,
A)we need to apply annual compounding.
B)we need to know the actual compounding frequency.
C)we get an approximation of the actual value.
D)we get a different result compared to calculations made with the nominal rate and the actual compounding frequency.

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Multiple Choice

Q 37Q 37

If I invest $100 per month for two years at 6% per annum compounded monthly,how much will I have after four years?
A)$2543.20
B)$5409.78
C)$2777.54
D)$2866.59

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Multiple Choice

Q 38Q 38

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)$4519.82
B)$8 574.96
C)$7 200.00
D)$3 993.09

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Multiple Choice

Q 39Q 39

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)$8 461.12
B)$38 461.12
C)$7 500
D)$8 288.45

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Multiple Choice

Q 40Q 40

An interest rate is quoted as 8% per annum compounded quarterly.What is the effective annual rate?
A)8.00%
B)8.22%
C)8.24%
D)8.34%

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Multiple Choice

Q 41Q 41

An interest rate is quoted as 8% per annum compounded daily.What is the effective annual rate?
A)8.33%
B)8.00%
C)8.30%
D)8.28%

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Multiple Choice

Q 42Q 42

An effective annual rate of 10.52% is equivalent to:
A)10% compounded daily.
B)10% compounded weekly.
C)10% compounded monthly.
D)10% compounded semi-annually.

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Multiple Choice

Q 43Q 43

An effective annual rate of 14.98% is equivalent to:
A)14% compounded daily.
B)14% compounded weekly.
C)14% compounded fortnightly.
D)14% compounded monthly.

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Multiple Choice

Q 44Q 44

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)$9128.55
B)$111 144.95
C)$11 111.11
D)$18 508.02

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Multiple Choice

Q 45Q 45

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)$111 978.54
B)$111 144.95
C)$9 950.11
D)$109 978.54

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Multiple Choice

Q 46Q 46

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)$1.72
B)$1.60
C)$2.72
D)$0.625

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Multiple Choice

Q 47Q 47

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)$4 800
B)$5086.39
C)$ 4 535.14
D)$ 4 512.57

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Multiple Choice

Q 48Q 48

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)$2124.34
B)$212.00
C)$2697.35
D)$2394.47

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Multiple Choice

Q 49Q 49

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)$4 512.57
B)$4 023.51
C)$4 400.14
D)$8 516.06

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Multiple Choice

Q 50Q 50

A philanthropist wishes to endow a scholarship of $10 000 per year for the next 20 years.The scholarship will be paid out of a trust fund at the end of each year,with the first payment occurring one year from now.How much would the philanthropist need to donate to the trust fund today if it is expected to earn 9% per annum?
A)$200 000.00
B)$93 315.45
C)$99 501.15
D)$91 285.46

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Multiple Choice

Q 51Q 51

The future value of an ordinary annuity paying $1000 for 20 years at an interest rate of 7% per annum is:
A)$10 594.01.
B)$40 995.49.
C)$38 992.10.
D)$42 300.74.

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Multiple Choice

Q 52Q 52

The future value of an ordinary annuity paying $3600 annually for 7 years at an interest rate of 12% per annum compounded annually is:
A)$36 320.44.
B)$38 900.29.
C)$35 600.20.
D)$37 826.98.

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Multiple Choice

Q 53Q 53

The present value of an ordinary annuity paying $100 for 12 years at an interest rate of 9.25% per annum is:
A)$856.39.
B)$707.14.
C)$829.61.
D)$843.05.

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Multiple Choice

Q 54Q 54

The present value of an ordinary annuity paying $5000 annually for 6 years at an interest rate of 5.75% per annum compounded yearly is:
A)$30 000.
B)$24 780.93.
C)$26 205.84.
D)$25 005.58.

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Multiple Choice

Q 55Q 55

A 10% five-year ordinary annuity with a future value of $2564.14 makes annual payments of:
A)$370.
B)$420.
C)$400.
D)$700.

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Multiple Choice

Q 56Q 56

A 7% per annum 10-year ordinary annuity with monthly compounding and a future value of $346169.61 makes monthly payments of:
A)$1000.
B)$1500.
C)$2000.
D)$2500.

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Multiple Choice

Q 57Q 57

A 3-year ordinary annuity with weekly compounding,a present value of $2412.96 and making weekly payments of $19.23 is trading at an annual interest rate of:
A)12% per annum compounded weekly.
B)15% per annum compounded daily.
C)14.5% per annum compounded daily.
D)13% per annum compounded monthly.

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Multiple Choice

Q 58Q 58

An investment paying $1000 in 1 year,$2000 in 2 years and $7000 in 3 years returning 10% per annum has a present value of:
A)$8129.39.
B)$6002.54.
C)$7210.20.
D)$7821.19.

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Multiple Choice

Q 59Q 59

An investment paying $2000 in 2 years,$6000 in 4 years and $5000 in 12 years at an interest rate of 5% per annum has a present value of:
A)$9534.46.
B)$6505.29.
C)$7354.21.
D)$12 090.49.

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Multiple Choice

Q 60Q 60

At an interest rate of 15% per annum,cash flows of $1000 today,$2000 in 1 year and $6000 in 2 years have a future value in 2 years of:
A)$8700.00.
B)$9622.50.
C)$9709.37.
D)$10 200.46.

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Multiple Choice

Q 61Q 61

At an interest rate of 12.5% per annum,cash flows of $2000 in 2 years,$12 000 in 7 years and $8000 in 20 years have a future value in 20 years of:
A)$73 730.20.
B)$71 593.52.
C)$80 147.38.
D)$70 994.74.

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Multiple Choice

Q 62Q 62

At an interest rate of 7% per annum,cash flows of $1000 in 5 years and $50 000 in 20 years have a future value in 60 years of:
A)$799 838.49.
B)$759 002.73.
C)$791 355.91.
D)$790 037.89.

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Multiple Choice

Q 63Q 63

Cash flows of $5000 in 2 years and $7000 in 4 years with a present value of $10 594.32 in 1 year are being discounted at an interest rate of:
A)5% per annum.
B)6% per annum.
C)7% per annum.
D)8% per annum.

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Multiple Choice

Q 64Q 64

Which of the following statements is NOT correct?
A)Bonds can be seen as annuities for the coupon payments.
B)A bond that trades above its face value is said to be sold at a premium.
C)Par value of a bond is its face value.
D)All bonds pay coupons.

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Multiple Choice

Q 65Q 65

The present value PV of a bond with a face value 1000,a coupon rate 5% paid annually and 2 years to maturity at the interest rate per annum 6% is:
A)981.67.
B)937.17.
C)934.50.
D)1093.40.

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Multiple Choice

Q 66Q 66

You have decided that when you retire in 20 years time,you will require a self-funded pension of $2500 per month for 25 years.In order to fund that pension how much per month will you need to save for the next 20 years at an interest rate of 6% per annum compounded monthly?

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Essay

Q 67Q 67

A couple are contemplating sending their 11-year-old son to boarding school for Years 11 and 12,commencing five years from now.If they plan to give their son $200 per month pocket money for two years,commencing five years from now,how much per month will they need to save at an interest rate of 6% per annum,compounded monthly? (Assume that the first payment of pocket money is made exactly five years from now.)

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Essay

Q 68Q 68

Briefly explain:
(a)the difference between the yield and the discount rate in relation to a commercial bill and
(b)why the yield will always be higher than the discount rate for a given commercial bill.

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Essay

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Essay

Q 70Q 70

Briefly explain why the future value of a bank deposit that earns simple interest will be less than a deposit of the same amount that earns compound interest at the same nominal rate.(Assume quarterly compounding.)

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Essay