Deck 2: A Review of Financial Mathematics

Question 1

What simple interest rate per year will give same future value at the end of 3 years as 10% p.a.compounded semi- annually?

A)10.00%
B)11.33%
C)10.25%
D)12.50%

Answer 1

11.33%

Question 2

What is the future value of a $1,000 invested for 20 years at an interest rate of 10% p.a.compounded quarterly?

A)$7209.57
B)$3000.00
C)$6727.50
D)$4709.21

Answer 2

$7209.57

Question 3

What is the present value of the following set of cash flows when the discount rate is 12% p.a.compounded monthly?

A)$1,308.10
B)$1,348.59
C)$1,398.45
D)$1,332.72

Answer 3

$1,308.10

Question 4

What is the present value of a perpetuity consisting of payments of $500 with an interest rate of 10% p.a.?

A)$5,000.00
B)$4,000.00
C)$3,000.00
D)$2,000.00

Question 5

What is the present value of an annuity consisting of 5 annual payments of $200 with an interest rate of 8% p.a.compounded annually and the first payment made immediately?

A)$862.43
B)$643.77
C)$889.68
D)$798.54

Question 6

The future value in 10 years of $1,000 invested at a 10% p.a.compounded annually interest rate will be the future value in 10 years of $1,000 invested at a 10% p.a.simple interest rate.

A)Less than
B)Less than or equal to
C)Greater than
D)Equal to
E)Greater than or equal to

Question 7

At the end of a 5- year period,the difference between the future value of $200 invested at 8% p.a.simple interest and $200 invested at 8% p.a.compounded annually interest will be .

A)$13.87
B)$22.10
C)$56.05
D)$213.87

Question 8

Which of the following statements is true?

A)Simple interest pays interest only on principle whereas compound interest also pays interest on interest.
B)Simple interest relates to future value whereas compound interest relates to present value.
C)Simple interest applies when an investor receives payment while compound interest applies when an investor makes payments.
D)Simple interest annualises rates while compound interest allows interest to be stated in any time period.
E)Simple interest relates to present value whereas compound interest relates to future value.

Question 9

What is X in the formula X = PV(1 + r)?

A)The present value of a single cash flow in one period's time
B)The future value of a single cash flow in one period's time
C)The future value of an annuity of PV cash flows
D)The present value of an annuity of PV cash flows

Question 10

What is the future value of $2,500 invested for 3 years at an interest rate of 11% p.a.compounded semi- annually?

A)$5,611
B)$4,429
C)$4,676
D)$3,447

Question 11

Asset A provides a cash flow of $100 in six years' time.Asset B provides a cash flow of $100 in four years' time.Which asset would a rational investor rather own?

A)Asset A
B)Asset B
C)Either asset A or asset B
D)Can't tell from the information provided

Question 12

Which of the following will yield the highest future value at the end of 5 years?

A)$1,200 invested at 11.5% p.a.compounded quarterly
B)$1,250 invested at 9.95% p.a.compounded daily
C)$1,300 invested at 10.25% p.a.compounded monthly
D)$1,400 invested at 12% p.a.simple interest

Question 13

What is the future value of $500 invested for 4 years at a simple interest rate of 5% p.a.?

A)$525
B)$575
C)$550
D)$600

Question 14

What is the future value of $3,400 invested for 7 years at a simple interest rate of 7.5% p.a.?

A)$21,250.00
B)$3,173.33
C)$5,185.00
D)$5,950.00

Question 15

What does the equation, (1 + r/m)^m - 1,calculate?

A)Compound interest rate over t periods where r is the effective simple interest rate
B)Compound interest rate over t periods where r is the number of compounding periods
C)The number of compounding periods over t years where r is the effective simple interest rate
D)Effective simple interest rate over t periods where r is the compound interest rate

Question 16

What is the present value of an annuity due consisting of 5 annual payments of $1,000 with an interest rate of 8% p.a. ,with the first payment occurring in 5 years' time?

A)$4,283.23
B)5,392.13
C)$2,935.30
D)$5,312.13

Question 17

What is the future value of $20 invested for 80 years at an annually compounded interest rate of 7% p.a.?

A)$11,200.00
B)$448.68
C)$4,495.66
D)$4,484.68

Question 18

What is the value of a share which is expected to pay a dividend of $0.11 every six months forever,on the basis that you intend to hold the shares forever,and the Australian ten- year bond rate today is 7.29%?

A)$2.20
B)$3.08
C)$0.60
D)$1.51

Question 19

What is the present value of $1,800 to be received in 1 year when the discount rate is 9.5% p.a.?

A)$1,643.84
B)$1,501.22
C)$1,487.60
D)$1,636.36

Question 20

Which of these answers best describes an ordinary annuity?

A)A series of equally sized regularly occurring cash flows extending n periods into the future,with the cash flows occurring at the end of each period
B)A series of equally sized regularly occurring cash flows extending n periods into the future,with the cash flows occurring at the start of each period
C)A series of equally sized regularly occurring cash flows extending indefinitely into the future,with the cash flows occurring at the start of each period
D)A series of equally sized regularly occurring cash flows extending indefinitely into the future,with the cash flows occurring at the end of each period

Question 21

Mr Riches has inherited a commercial building that is expected to yield the following cash flows for the next 5 years: However,Mr Riches would rather receive the same cash flow each year and he approached CDM Bank Ltd to sell the building in return for a fixed cash flow each year for 5 years.CDM Bank Ltd has agreed to this arrangement.If CDM Bank Ltd is using an interest rate of 10% p.a.compounded monthly to value the building how much would they be willing to pay Mr Riches each year?

A)$2,663,498.55
B)$2,687,456.15
C)$2,648,984.45
D)$2,653,899.02

Question 22

Which of the following statements is most true?

A)There is a relationship between the future value of investment and the effect of compounding frequency.At low interest rates,increases in compounding frequency will decrease the future value.
B)There is a relationship between the future value of investment and the effect of compounding frequency.At high interest rates,increases in compounding frequency will decrease the future value.
C)Regardless of the value of the interest rate,increasing the compounding frequency will decrease the future value.
D)Regardless of the value of the interest rate,increasing the compounding frequency will increase the future value.

Question 23

Over a one- year period,the difference between the future value of $500 invested at 15% p.a.simple interest and $500 invested at 15% p.a.annually compounded interest will be .

A)$150.00
B)$1.50
C)$15.00
D)Nothing

Question 24

What is the present value of an ordinary annuity consisting of 5 annual payments of $1,000 with an interest rate of 8% p.a. ,with the first payment occurring in 5 years' time?

A)$4,918.64
B)$4,992.71
C)$2,717.37
D)$3,696.95

Question 25

What is the future value of $200 invested for 10 years at an annually compounded interest rate of 2% p.a.?

A)$438.00
B)$243.80
C)$254.60
D)$242.00

Question 26

What is the future value of $4,000 invested for 8 years at an annually compounded interest rate of 9.25% p.a.?

A)$8,250.66
B)$4,074.00
C)$1,840.06
D)$8,117.67

Question 27

What is the future value of $100 continuously compounded at a rate of 8% p.a.for 9 months?

A)$106.18
B)$108.32
C)$110.56
D)$102.56

Question 28

What is the future value of $1,000 continuously compounded at a rate of 10% p.a.for 5 years?

A)$1,610.51
B)$1,648.72
C)$1,498.43
D)$1,500.00

Question 29

Which of these responses would describe an asset's future value?

A)The accumulated value
B)The value at some point in the future of a present amount invested at some interest rate
C)The current value of one or more future cash payments,discounted at some interest rate
D)None of the above

Question 30

An investor has the possibility to deposit $500 in one of two potential bank accounts.Account A offers an interest rate of 5% p.a.compounded semi- annually whilst Account B offers an interest rate of 4.9% p.a.compounded quarterly.Which will yield the highest future value?

Question 31

What is the present value of an ordinary annuity consisting of 15 annual payments of $50 with an interest rate of 3.5% p.a.compounded quarterly?

A)$575.87
B)$3,486.36
C)$1,159.29
D)$2,326.24

Question 32

The present value of an annuity due is always less than the present value of an otherwise identical ordinary annuity.

Question 33

What is the future value of an ordinary annuity consisting of 10 annual payments of $100 with an interest rate of 10% p.a.compounded weekly?

A)$1,593.70
B)$1,632.97
C)$1,457.90
D)$1,873.23

Question 34

What is the future value of $800 invested for 10 years at a simple interest rate of 2% p.a.?

A)$816
B)$1,134
C)$1,040
D)$960

Question 35

You have just won first division in the State lottery,and have a choice between three alternatives as to how your prize is to be received.You can get $100,000 now,or $10,000 per year in perpetuity,or $50,000 now and $150,000 at the end of 10 years.If the appropriate discount rate is 12% per annum,which option should you choose?

Question 36

The future value of an ordinary annuity consisting of 10 annual payments is $1593.74.The interest rate is 10% p.a.compounded annually;therefore the amount of each payment must be how much?

A)$120.00
B)$90.00
C)$110.00
D)$100.00

Question 37

Why is it not possible to determine the future value of a perpetual stream of cash flows?

Question 38

What is the present value of $800 to be received in 5 years' time when the discount rate is 9% p.a.compounded quarterly?

A)$519.95
B)$512.65
C)$509.75
D)$515.69

Question 39

What is the future value of $100 invested for 10 years at an interest rate of 2% p.a.compounded annually?

A)$123.77
B)$120.00
C)$122.11
D)$121.90

Question 40

You are considering the purchase of new car using a financing arrangement.Under the deal you must make a $10,000 deposit immediately and then monthly payments of $800 for a period of 48 months.The monthly payments are made at the end of each month.The interest rate is 12% p.a.compounded monthly.What is the effective cost of the car?

Question 41

A bank that offers depositors a 10% p.a.rate compounded semi- annually is using continuous compounding to calculate depositors' interest payments.

Question 42

The future value compounding formula is FV = PV (1 + r )ⁿ.

Question 43

Holding all other factors constant,increasing the frequency of the compounding period will increase the future value of an initial investment.

Question 44

The amount of interest earned each year does not change when interest is compounded.

Question 45

The effective simple interest rate will always be higher than the compound interest rate if the compounding interval is greater than one.

Question 46

An ordinary annuity has unequal cash flows.

Question 47

A deferred annuity is an annuity due that starts at a date more than one period into the future.

Question 48

The effective rate of interest decreases as the compounding frequency increases.

Question 49

A perpetuity is an annuity that lasts forever.

Question 50

The cash flows of an ordinary annuity occur at the end of each period.

Question 51

An annuity due has cash flows that occur at the end of each period.

Question 52

A constant dividend paying share is an example of an ordinary annuity.

Question 53

Interest earned on long- term bonds is an example of an annuity.

Question 54

The future value of a future cash flow will always be lower than the present value if the interest rate used is anything other than zero.