Deck 8: Mathematics of Finance: An Introduction to Basic Concepts and Calculations

Question 1

What is the future value of $12 000 on deposit for four years at 7.00% per annum simple interest?

A) $3360.00
B) $12 336.00
C) $15 360.00
D) $15 729.55

Answer 1

C

Question 2

If a company sells (discounts)a bank bill with a face value of $100 000,a term to maturity of 90 days,and a yield of 7.23% per annum,how much will the company raise on the issue? (Ignore transaction fees.)

A) $84 869.90
B) $98 248.49
C) $98 269.99
D) None of given answers.

Answer 2

B

Question 3

If you borrow $100 000 for 90 days with simple interest of 6.2% per annum,what is the total amount of interest paid on the loan?

A) $1528.77
B) $6200.00
C) $620.00
D) $15 287.67

Answer 3

A

Question 4

A 90-day promissory note with a face value of $500 000 is issued at a yield of 7.789% per annum.Calculate its price.

A) $379 971.77
B) $419 442.84
C) $490 578.08
D) $490 711.67

Question 5

What is the present value of $1 million payable in 90 days at 8.00% per annum simple interest?

A) $835 240.27
B) $974 372.66
C) $980 655.56
D) $1 002 747.25

Question 6

If you receive $100 000 back as principal and interest for an investment of $92 368 that you made six months earlier,what simple rate of interest has been earned on your investment?

A) 7.63% per annum
B) 15.48% per annum
C) 16.16% per annum
D)
D)16.75% per annum

Question 7

If you invest $7500 for a year at 7.4% per annum simple interest,what is the value of your investment at the end of the year?

A) $555.00
B) $5550.00
C) $8055.00
D) $13 050.00

Question 8

When a company sells a commercial bill,this means the company:

A) lends funds.
B) lends a commercial bill.
C) issues a commercial bill.
D) invests in a commercial bill.

Question 9

The term 'simple',with regard to interest,refers to the fact that:

A) the interest calculation is easy to work out.
B) principal repayment is guaranteed.
C) interest payments are guaranteed.
D) interest is calculated on the initial principal only.

Question 10

The market convention to use a 360-day year in the financial markets applies in:

A) the United Kingdom.
B) Australia.
C) the United Kingdom and euromarkets.
D) the United States and euromarkets.

Question 11

When a company discounts a commercial bill,this means the company:

A) borrows funds.
B) buys a commercial bill.
C) lends surplus funds.
D) invests in commercial bills.

Question 12

If you invest $1200 for two years at 6.9% per annum simple interest,what is the value of your investment at the end of the two years?

A) $165.60
B) $1365.60
C) $1656.00
D) $2856.00

Question 13

If you receive $100 000 back as principal and interest at the end of the year for an initial investment of $93 456 at the start of the year,what interest has been earned on your investment?

A) 6.54%
B) 65.4%
C) 7.00%
D) 70.00%

Question 14

If a company sells (discounts)a bank bill with a face value of $500 000,a term to maturity of 120 days,and a yield of 8.45% per annum,how much will the company raise on the issue? (Ignore transaction fees.)

A) $391 295.03
B) $445 312.02
C) $486 485.05
D) $486 302.48

Question 15

If you invest $1600 for a year at 6.8% per annum simple interest,how much interest will you earn?

A) $10.80
B) $108.00
C) $1088.00
D) $1708.80

Question 16

If you receive $10 000 back as principal and interest at the end of two years for an initial investment of $9127 at the start of the term,what is the yield on your investment?

A) 4.37% per annum
B) 4.78% per annum
C) 8.73% per annum
D) 9.57% per annum

Question 17

If you invest $13 500 for 18 months at 6.9% per annum simple interest,what is the value of your investment at the end of the 18 months?

A) $14 431.50
B) $14 897.25
C) $21 647.25
D) $22 815.00

Question 18

When a company discounts a commercial bill to obtain funds,this means the company:

A) issues a commercial bill.
B) lends funds.
C) buys a commercial bill.
D) invests in commercial bills.

Question 19

If the current yield on 180-day Treasury notes is 6.42% per annum,what price per $100 of face value would an investor pay to purchase them?

A) $75.95
B) $96.93
C) $96.94
D) $99.98

Question 20

If you invest _______ to earn simple interest of 6.8% per year,you will receive $12 375 at the end of two years.

A) $4759.62
B) $5156.25
C) $9728.77
D) $10 893.49

Question 21

What is the future value in six years of $10 000 invested today,compounding at 6.87% per annum?

A) $14 122.00
B) $14 898.24
C) $15 128.26
D) $23 051.04

Question 22

You are considering an investment that will pay a lump sum of $50 000 at the end of six years and you decide that 9% per annum compounded monthly is an appropriate discount factor.What is the value of the investment in today's dollar terms?

A) $31 508.48
B) $32 496.57
C) $31 934.98
D) $47 846.89

Question 23

What is the future value in four-and-a-half years of $5000 invested today at 9.50% compounded semi-annually?

A) $6161.17
B) $7522.00
C) $7592.00
D) $9875.00

Question 24

What is the present value of the following cash flow stream,discounted at 6.5% per annum,compounded monthly?
Year 1:
$1000; Year 2:
$1500; Year 3:
$2000; Year 4:
$2500

A) $5844.58
B) $5863.11
C) $5874.79
D) $5986.23

Question 25

If your deposit of $30 000 becomes $30 919 at the end of 120 days,what is the annual yield earned?

A) 9.04%
B) 9.19%
C) 9.23%
D) 9.32%

Question 26

The idea of compound interest refers to:

A) the payment of interest on previously earned interest.
B) investing for multiple periods in one year.
C) earning interest only on the initial investment.
D) changing interest rates during an investment.

Question 27

The main difference between an annuity and an annuity due lies in the:

A) number of payments.
B) time of the first payment.
C) interest rate.
D) frequency of payments.

Question 28

If interest rates are 8.21% per annum,compounded annually,the present value of $31 000 received at the end of three years is:

A) $2819.17
B) $9549.33
C) $24 465.80
D) $28 647.99

Question 29

If you borrow $11 000 for four years at an annually compounding rate of 8.2% per annum,what is the total interest on the loan if the interest due is added to the principal over the period and repaid at the maturity date?

A) $2933.96
B) $3608.00
C) $3842.51
D) $4076.54

Question 30

What is the simple annualised interest rate on a company transaction to raise $100 000 financing by drawing a bank bill with a face value of $104 000,payable in 120 days?

A) 4%
B) 12%
C) 12.17%
D) 12.67%

Question 31

If you borrow $20 000 for four years at an interest rate of 7.23% per annum,with the interest compounding quarterly,how much will you have to pay at the end of the period?

A) $21 485.68
B) $26 442.06
C) $25 784.00
D) $26 638.29

Question 32

If your investment of $5000 with the bank carries a compound interest of 8.75% per annum,the value of your investment at the end of three years is:

A) $1430.69
B) $6312.50
C) $6430.69
D) $5437.50

Question 33

A bank bill with a face value of $500 000 and 90 days to maturity is purchased with a yield to maturity of 6.92% per annum.After the bill has been held for 28 days,it is sold at a yield of 6.78% per annum.What is the holding period yield for the holder of the note?

A) 3.23% per annum
B) 7.11% per annum
C) 7.15% per annum
D) 7.51% per annum

Question 34

An $8000 bank deposit earning compound interest of 8.21% per annum grows to _______ in 5.25 years.

A) $11 284.00
B) $12 058.14
C) $12 105.81
D) $16 019.15

Question 35

If you invest $12 000 for 4.75 years at 7.88% per annum,with interest compounded monthly,what will your total investment be worth at the end of the period?

A) $12 378.94
B) $15 476.29
C) $16 232.40
D) $17 426.34

Question 36

When will a future value calculated with a simple interest rate exceed a future value calculated with compound interest at the same rate?

A) When the interest rate exceeds 100% per annum
B) When the investment period exceeds 50 years
C) When the initial deposit exceeds $1 billion
D) This is not possible with positive interest rates

Question 37

A finite stream of regular cash flows over a given period is known as a/an:

A) perpetuity.
B) annuity.
C) debenture.
D) allowance.

Question 38

In regard to an annuity,if the first cash flow is made immediately,it becomes:

A) a simple annuity.
B) an ordinary annuity.
C) an annuity due.
D) the present value of an annuity.

Question 39

What is the price today of an investment that will pay the single sum of $20 000 after three and a half years if the discount rate is 7.64% per annum,compounded annually?

A) $2743.37
B) $15 456.89
C) $15 780.00
D) $16 036.48

Question 40

A company invests its surplus funds by buying a commercial bill with a face value of $100 000,at a current yield to maturity of 7.35% per annum and 120 days to maturity.After 45 days,the bill is sold at a yield of 6.84% per annum.What rate of return did the company earn on the bill?

A) 4.85% per annum
B) 8.01% per annum
C) 8.09% per annum
D) 8.90% per annum

Question 41

The present value of an ordinary annuity with equal monthly payments of $300 over the next four years,assuming market interest rates are 12% per annum,is:

A) $911.20
B) $1170.59
C) $11 392.19
D) $18 366.78

Question 42

What is the current price of a financial security that pays a fixed coupon of 10.2% per annum per $100 face value,compounding half-yearly and maturing in four years,when current yields in the market are 8.6% per annum?

A) $103.9575
B) $70.3185
C) $103.887
D) $132.8295

Question 43

The present value of an annuity of $11 000,received at the end of every year for ten years,where the required rate of return is 5.6% per annum,compounded annually,is:

A) $6379.01
B) $7051.28
C) $8251.76
D) $82 517.62

Question 44

Calculate the effective annual interest rate if your bank quotes you 10% per annum,compounded quarterly.

A) 14.01%
B) 10.38%
C) 10%
D) 2.50%

Question 45

Calculate the effective annual interest rate corresponding to 9.6% per annum,compounded monthly.

A) 10.03%
B) 9.6%
C) 8.0%
D) 6.9%

Question 46

If the effective annual interest rate is known to be 19.4% on a debt that has quarterly payments,what is the annual percentage rate?

A) 19.40%
B) 19.10%
C) 18.13%
D) 18.00%

Question 47

If you are saving for an overseas trip and put $400 every month into an account paying 6.8% per annum,compounding monthly,how much will you have at the end of 3.25 years?

A) $5014.43
B) $16 907.41
C) $17 001.84
D) $17 403.22

Question 48

Calculate the effective annual interest rate if you are quoted 8% per annum,compounded half yearly.

A) 8.27%
B) 8.16%
C) 8.0%
D) 4.0%

Question 49

If the effective annual interest rate is known to be 16.0% on a debt that has monthly payments,what is the annual percentage rate?

A) 16.00%
B) 14.93%
C) 12.45%
D) 1.33%

Question 50

What is the current price of an existing Treasury bond that pays a fixed coupon of 6.4% per annum per $100 face value,compounding half-yearly,and maturing in four years? Current market yields are 6.8% per annum.

A) $22.0888
B) $44.1775
C) $76.5307
D) $98.6195

Question 51

If you make an investment and agree to pay regular monthly payments of $450 at the end of the next twelve months,starting one month from today,what is the present value of this investment if the interest rate is 8.4% per annum compounded monthly?

A) $3322.06
B) $4916.30
C) $5162.12
D) $5198.25

Question 52

The present value of an ordinary annuity of $1000 each year for six years,assuming current market interest rates,is:

A) $1625.20
B) $2982.64
C) $4596.19
D) $4956.19

Question 53

If the interest rate is 6.9% per annum,compounded annually,what is the future value of a five-year ordinary annuity with yearly payments of $4000?

A) $5584.04
B) $18 709.07
C) $22 957.10
D) $30 984.06

Question 54

If the interest rate is 7.4% per annum,compounding quarterly,what is the future value of a six-year ordinary annuity with quarterly payments of $4000?

A) $28 903.12
B) $85 938.40
C) $62 647.89
D) $103 126.09

Question 55

What is the current price of an existing debenture with a face value of $1000 that pays a fixed coupon of 8.4% per annum,compounded annually,and maturing in five years? Current yields in the market are 6.6% per annum.

A) $941.65
B) $999.96
C) $1016.26
D) $1049.54

Question 56

Calculate the effective annual interest rate if you are quoted 8% per annum,compounded every three months.

A) 11.10%
B) 8.24%
C) 8.22%
D) 8.00%

Question 57

You take out a loan to buy a property and agree to pay $53 000 one year from now,another $53 000 two years from now,and a final payment of $53 000 three years from now.If your interest rate is fixed at 8.5% per annum,compounded annually,calculate the value of the loan today.

A) $135 363.19
B) $139 426.13
C) $146 543.78
D) $157 515.25

Question 58

An investor plans to save $1000 per year for the next ten years as a retirement fund,and expects to earn 8.4% per annum,compounded monthly over the period,on all invested funds.How much will the investor have at the end of ten years?

A) $187 085.48
B) $296 035.24
C) $126 882.77
D) $153 178.10

Question 59

The present value of an annuity of $800,received at the end of every month for 20 years,where the required rate of return is 6.5% per annum,compounded monthly,is:

A) $33 366.03
B) $43 367.94
C) $107 300.02
D) $192 000.00

Question 60

A property investor receives rental payments of $1900 at the start of each month for five years.If the required rate of return is 7.2% per annum,compounded monthly,what is the value of the property investment today?

A) $83 067.50
B) $90 092.50
C) $95 498.05
D) $96 071.04

Question 61

Explain the differences(s)between an interest rate and a rate of return.

Question 62

The amount that an investor puts up initially for a commercial bill is called the principal.

Question 63

Distinguish between simple interest and compound interest.

Question 64

If an investor purchases a commercial bill with a face value of $100 000 with a yield of 7.00% per annum and then,in 60 days,sells it at a yield of 7.50% per annum,the investor will make a capital gain on the sale of the bill.

Question 65

If compounding of interest occurs more often than annually,explain how you would compare three interest rates of the same amount:
one that is quoted annually,one semi-annually and one quarterly.At which rate would you expect the same investment amount to grow the most over ten years?

Question 66

Accumulation of final amounts under simple interest happens at a slower rate than with compounding interest.

Question 67

The principal of a six-month bank deposit is the amount you receive at the end of its term.

Question 68

If a commercial bill is sold into a market in which its yield works out higher than the yield that prevailed at the original purchase date,a capital gain would have been made.

Question 69

When a company issues a commercial bill it is said to discount it.

Question 70

In relation to interest rates,explain what a yield is.

Question 71

When a company obtains an interest-only business bank loan and is required to make annual interest payments on the principal borrowed and repay the full principal at the maturity date,the type of interest is called simple interest.

Question 72

When a holder of a commercial bill sells it before its maturity date the return to the holder is called the holding period return.

Question 73

The euromarkets,unlike those of the US,follow the market convention that a per-annum rate relates to a 365-day year.

Question 74

If an investor purchases a commercial bill with a face value of $100 000 with a yield of 7.00% per annum and then,in 60 days,sells it at a yield of 6.70% per annum,the investor will make a capital loss on the sale of the bill.

Question 75

Distinguish between an ordinary annuity and an annuity due.Give examples.