Deck 3: The Time Value of Money: An Introduction to Financial Mathematics

Question 1

You have borrowed $1000 from a friend to pay for unforeseen car repairs,with an agreement to pay interest at an annual rate of 18%,compounding daily.If you repaid your friend after 90 days,how much would you need to repay?

A)$1044.38
B)$1045.00
C)$1045.37
D)$1043.56

Answer 1

$1045.37

Question 2

The interest rate where interest is charged at the same frequency as the quoted interest rate is the:

A)nominal interest rate.
B)real interest rate.
C)compound interest rate.
D)effective interest rate.

Answer 2

effective interest rate.

Question 3

A financial contract is:

A)a piece of advice provided by financial planners.
B)an agreement that involves only book entries and does not result in any cash flows.
C)an arrangement,agreement or investment that produces cash flows
D)an agreement that results in a profit for the businesses concerned.

Answer 3

an arrangement,agreement or investment that produces cash flows

Question 4

The value,as at the date of the final cash flow promised in a financial contract,that is equivalent to the stream of promised cash flows is the:

A)present value of a contract.
B)future value of a contract.
C)terminal value of a contract.
D)discounted value of a contract.

Question 5

Assume that on 1 January 2011 you deposit $1000 into a savings account that pays 8% p.a.If the bank compounds interest annually,how much will you have in your account on 1 January 2014?

A)$1292.43
B)$1357.61
C)$1259.71
D)$1439.16

Question 6

If a term deposit paid an interest rate of 24% p.a.over the past six months,and the current balance is $1008,what was the amount initially invested?

A)$812.90
B)$681.08
C)$900.00
D)$975.00

Question 7

A process by which,through the operation of interest,a present sum becomes a greater sum in the future is:

A)the additive principle.
B)the accumulation principle.
C)the compounding principle.
D)the discounting principle.

Question 8

A principle that a dollar is worth more the sooner it is to be received,all other things equal,is:

A)the time value of money.
B)the value of money.
C)Fisher's effect.
D)net present value.

Question 9

An annuity in which the first cash flow is to occur after a time period that exceeds the time period between each subsequent cash flow is known as a/an:

A)deferred annuity.
B)growth annuity.
C)ordinary annuity.
D)annuity due.

Question 10

The amount that corresponds to today's value of a promised future sum can be shown as:

A)
B)
C)
D)

Question 11

Suppose you deposited $250 at the end of 2011,2012,2013 and 2014.How much would you have in your account on 1 January 2015,based on annual compounding of 8% by your bank?

A)$1025.25
B)$1235.53
C)$1183.53
D)$1126.53

Question 12

What will your investment be worth in 10 years if you invest $15 000 at 12.5% p.a. ,payable at maturity,and your tax rate (paid annually)is 30 cents in the dollar?

A)$34 097
B)$48 710
C)$32 473
D)$34 704

Question 13

The rate of return can be shown as:

A)
B)
C)
D)

Question 14

An annuity in which the first cash flow is to occur immediately is known as a/an:

A)ordinary annuity.
B)ordinary perpetuity.
C)annuity due.
D)growth annuity.

Question 15

You have $10 000 to invest.If you invest it at 11.2% p.a.for six months,then invest the initial $10 000 together with any interest for a further 12 months at 12.7% p.a. ,what will be the value of your investment at the end of the 18-month period?

A)$11 901.12
B)$12 532.24
C)$11 830.00
D)$12 241.36

Question 16

Calculate the average annual rate of return on an investment of $1000 that accumulates to $2005 in five years' time.

A)14.93%
B)8.8%
C)100.5%
D)17.63%

Question 17

Assume that on 1 January 2011 you deposit $1000 into a savings account that pays 8% p.a.If the bank compounds interest quarterly,how much will you have in your account on 1 January 2014?

A)$1268.24
B)$1349.13
C)$1301.15
D)$1483.09

Question 18

If you invest $47 000 for five years at 9.7% p.a.(interest paid annually and then reinvested),what is the value of your investment at the end of the five-year period?

A)$81 910.13
B)$74 667.39
C)$56 560.22
D)$62 046.56

Question 19

The calculation that expresses the ratio of net cash inflows to net cash outflows produced by a financial contract is known as:

A)net present value.
B)net profit.
C)internal rate of return.
D)rate of return.

Question 20

A method of calculating interest in which,during the entire term of the loan,interest is computed on the original sum borrowed is the:

A)present value method.
B)simple interest method.
C)compound interest method.
D)interest rate method.

Question 21

Kristy has to make rental payments of $1000 at the start of every month,throughout the four-year duration of her university course.Her university fees are $4000 to be paid at the start of each year.She earns $1500 per month (paid at the end of each month)from a part-time job.Assume an interest rate of 8% p.a.and that she keeps the part-time job for the next four years.How much money,in present value terms,can she withdraw each month for the next four years?

A)$144
B)$126
C)$55
D)$177

Question 22

Assume that you will require $1000 in four years' time.Suppose that you can afford to deposit only $186.29 at the end of each year,the first deposit to be made in one year's time.What interest rate would you require to reach your target if the bank compounds annually?

A)15% p.a.
B)18.5% p.a.
C)20% p.a.
D)22.5% p.a.

Question 23

Calculate the present value of the following cash flows assuming they occur at the end of each year and the interest rate is 12% p.a.:
Year 0,($12 000);Year 1,$5670;Year 2,$11 250.

A)$2030.93
B)$26 030.93
C)$28 920
D)($1163.19)

Question 24

What is the present value of the following cash flow stream,discounted at 7% p.a.: Year 1,$100;Year 2,$400;Years 3 through 20,$300?

A)$2859.20
B)$3563.40
C)$3078.63
D)$2782.40

Question 25

Karen has borrowed $12 000 in student loans at an annual interest rate of 9%.If she repays $1500 per annum,how long (to the nearest year)will it take to repay the loan?

A)10 years
B)15 years
C)12 years
D)17 years

Question 26

Debt Ltd borrowed $100 000 from its local bank to finance the purchase of new equipment.Annual payments are required over five years at a fixed interest rate of 10% p.a.How much is each annual payment?

A)$27 398.18
B)$20 000.00
C)$26 379.75
D)$24 444.12

Question 27

What is the present value of $500 payable in 10 years' time if the interest rate is 6% p.a.?

A)$290.50
B)$335.60
C)$895.40
D)$279.20

Question 28

What is the effective annual interest rate corresponding to a nominal interest rate of 10% p.a. ,compounding continuously?

A)10.5%
B)10.9%
C)12.5%
D)13%

Question 29

Five years ago,you entered into a loan agreement to borrow $100 000.The loan was to be paid off over 20 years through equal monthly instalments.If the interest rate was fixed at 12% p.a.for the entire loan term,how much do you pay per month?

A)$949
B)$1066
C)$1101
D)$1223

Question 30

If the nominal interest rate is 12% p.a.and the inflation rate is expected to be 5% p.a. ,what is the real rate of interest?

A)106.7%
B)6.7%
C)7%
D)8.2%

Question 31

You want to deposit amounts in the bank at the end of 2011,2012,2013 and 2014,so that you have $1259.71 in your account on 1 January 2015.Calculate how large each of your payments would need to be if the bank compounds quarterly at 8% p.a.

A)$279.56
B)$259.83
C)$284.19
D)$314.93

Question 32

If a term deposit offers an interest rate of 10% p.a. ,compounding continuously,how much will an initial investment of $50 000 be worth after one year?

A)$55 258
B)$135 914
C)$62 519
D)$98 352

Question 33

Calculate the effective annual interest rate corresponding to 12% p.a. ,compounded quarterly.

A)11.9%
B)12.55%
C)12.45%
D)12.71%

Question 34

What is the implied interest rate if you borrow $85 000 and promise to pay back $201 229 at the end of 10 years?

A)9% p.a.
B)18% p.a.
C)11% p.a.
D)13% p.a.

Question 35

Debt Ltd borrowed $100 000 from its local bank to finance the purchase of new equipment.Annual payments are required over five years at a fixed interest rate of 10% p.a.How much is each annual payment?

A)$27 398.18
B)$20 000.00
C)$26 379.75
D)$24 444.12

Question 36

You have a goal to raise $1000 in four years' time.If your mother gives you $400 at the end of the first year,you make six deposits of equal amounts every six months thereafter,and all the money is deposited in a bank,which pays 8% p.a. ,compounded semi-annually,how large must each of the six payments be for you to reach your target?

A)$74.46
B)$65.55
C)$82.74
D)$77.26

Question 37

Calculate the value of an investment at the end of its fourth year if the initial investment is $10 000 and it produces the following annual rates of return: Year 1,gain 15%;Year 2,gain 17%;Year 3,loss 5%;Year 4,gain 4%.

A)$14 295
B)$13 100
C)$13 293
D)$11 957

Question 38

Matthew earns $10 000 per month for the next 25 years,after which he retires.During the first five years of retirement,he withdraws $6000 at the start of each month,after which he dies.His son,Sean,inherits the remainder of Matthew's savings.It is further stipulated in Matthew's will that Sean will be paid the money in equal payments at the start of every month,for the next 20 years.Given a fixed interest rate of 9% p.a. ,calculate the amount of the monthly payments that Sean receives.

A)$98 250
B)$97 340
C)$98 270
D)$97 519

Question 39

John has just been employed by a prestigious firm,drawing an annual salary of $300 000,paid at the end of each year.He plans to work for five years before retiring.He buys a new luxury home with mortgage repayments of $5000 per month for the next 20 years (payable at the end of each month),and donates $10 000 per annum forever to his favourite charity.What annual amount,in present value terms,can John withdraw for the first five years of his retirement from the remainder of his savings? Assume an annual interest rate of 6% p.a.

A)$93 926
B)$246 819
C)$94 754
D)$112 754

Question 40

Calculate the present value of a government security that promises to pay $100 p.a.forever,assuming an interest rate of 11% per annum.

A)$90
B)$1100
C)$909
D)Infinity.

Question 41

In an interest-only loan,the principle reduces by a small amount at first,and more rapidly towards the end of the loan.

Question 42

An individual borrowed $100 000 at a fixed interest rate of 12% p.a.for the entire loan term of 20 years.If the loan is to be repaid through equal monthly instalments,then the regular repayment to the nearest dollar is $1101.

Question 43

If you have a choice to earn simple interest on $20 000 for three years at 9% or annually compounding interest at 8.5% for three years which one will pay more interest and by how much?

A)Simple interest by $50.00
B)Compound interest by $122.97
C)Compound interest by $145.78
D)Simple interest by $150.00

Question 44

The nominal interest rate is difference between the inflation rate and the real rate of interest.

Question 45

If expected inflation over the next year is 2%,and CBank requires a real rate of return of 4% per annum on housing loans,what is the nominal rate of return that CBank will charge on home loans?

Question 46

The ______ interest rate is an interest rate calculated after taking out the effects of inflation.

Question 47

Continuous interest rates are an example of where the future sum grows _____________.

Question 48

Joe has to pay $50 000 in 1.5 years' time.If the interest rate is 15% p.a. ,compounded continuously,how much does she owe in present value terms?

A)$46 387
B)$49 077
C)$39 926
D)$37 041

Question 49

You are planning a six month around-the-world trip in 2 years' time.You estimate that you will need $30 000 to pay for the trip.To accumulate this future amount you plan to deposit an equal amount in the bank each month,which will earn 9% nominal interest per annum compounded monthly.Your first payment will be made at the end of the first month.
a.How much must you deposit each month to accumulate the $30 000?
b.What is the effective annual rate of interest that corresponds to this nominal rate?
c.If you could instead make a lump sum payment today instead of monthly payments,how much would this sum have to be to reach $30 000 in two years if it earns a nominal 9% per annum compounded monthly?

Question 50

A principle-and-interest loan is a common example of an __________ annuity.

Question 51

The annuity where the cash flows continue forever is called a ________.

Question 52

Peter borrowed $5000 and 18 months later repays the loan with a single payment of $6400.
a.What is the implied annual simple interest rate?
b.What is the implied annual compound interest rate?

Question 53

A lender offers a nominal interest rate on a loan of 6% p.a.compounding quarterly.This corresponds to an effective interest rate of 6.136%.

Question 54

The term ______________ is used to describe the 'rate of return' when the financial contract is in the form of debt.

Question 55

An __________ interest rate is one where the frequency of payment does not match the time period specified by the interest rate.

Question 56

An individual is offered the sum of $100 000 to be received after 5 years.If the relevant interest rate is 8% p.a. ,compounding annually,then the present value of this promised sum is $68 058.32.

Question 57

You have an outstanding car loan of $300 per month for the next 2 years.As you are finishing your studies this year,it would be better if you could pay the full sum at the end of two years.If the interest rate on the loan is 6% per annum (compounded monthly),what final sum would the bank require at the end of two years so that it is indifferent between the two methods of payment?

Question 58

The distinguishing feature of an annuity due is that the time period between the payment of each successive cash flow differs to the frequency with which the interest compounds.

Question 59

Your parents give you $120 per week for living expenses while you are doing a three-year degree in finance.If the interest rate is 6.5% per annum,what is this cash flow worth when you start your degree?

A)$15 125
B)$16 998
C)$26 026
D)$27 330

Question 60

What is the difference between daily and monthly compounding for a nominal interest rate of 7% per annum?

A)0.06%
B)0.04%
C)0.02%
D)0.01%

Question 61

You buy a perpetuity that makes one payment at the end of each year.If you invest $10 000 and the interest rate is 5% per annum,what is the payment each year?

Question 62

You have borrowed $300 000 over 30 years in order to purchase your first home.The loan repayments are monthly at a nominal interest rate of 6.5% per annum compounded monthly.
a.What are the repayments?
b.If after two years the interest rate rises to 7.5% per annum what are the new monthly repayments?
c.If the interest rate does not change but from the beginning you decide to repay $2500 per month how long will it take to repay the loan? What amount would be the final repayment?