Deck 5: Financial Mathematics

Question 1

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

Answer 1

False

Question 2

A commercial bill is priced using simple interest.

Answer 2

True

Question 3

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.

Answer 3

True

Question 4

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

Question 5

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

Question 6

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

Question 7

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

Question 8

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.

Question 9

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

Question 10

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

Question 11

Interest is the rent or price charged for the temporary use of someone else's money.

Question 12

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

Question 13

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.

Question 14

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

Question 15

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

Question 16

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.

Question 17

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

Question 18

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

Question 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.

Question 20

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

Question 21

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

Question 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

Question 23

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

Question 24

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%

Question 25

Which of the following financial instruments does NOT apply simple interest?

A)Saving account
B)Term deposit
C)Loan between relatives
D)Annuity

Question 26

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

Question 27

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.

Question 28

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

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

Question 30

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.

Question 31

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%

Question 32

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

Question 33

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

Question 34

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

Question 35

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

Question 36

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

Question 37

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%

Question 38

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.

Question 39

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%.

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

Question 41

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.

Question 42

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

Question 43

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.

Question 44

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.

Question 45

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

Question 46

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.

Question 47

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

Question 48

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.

Question 49

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.

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

Question 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.

Question 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.

Question 53

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.

Question 54

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

Question 55

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%

Question 56

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

Question 57

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

Question 58

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.

Question 59

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.

Question 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.

Question 61

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.)

Question 62

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.)

Question 63

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.

Question 64

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.

Question 65

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.

Question 66

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.

Question 67

Briefly describe why a dollar is worth more the sooner it is received.

Question 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.

Question 69

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?

Question 70

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.