Financial math practice 1 Questions, Solutions and Comments PDF

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Financial math practice 1 Questions, Solutions and Comments...

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FINANCIAL CALCULATION PRACTICE 1 Section A : Multiplie Choice Questions 1. A lender lends $10,000, which is to be repaid in annual payments of $2000 for 6

years. Which of the following shows the timeline of the loan from the lender's perspective? A)

Year 1 $0

Year 2 Year 3 $2000 $2000

Year 4 Year 5 $2000 $2000

Year 6 $2000

B)

Year 1 -$10,000

Yea r 2 $2000

Year 3 Year 4 $2000 $2000

Year 5 $2000

Yea r 6 $2000

C)

Year 0

Year l Year 2

Year 3 Year 4

Year 5

Year 6

-$10,000

$2000

$6000

$10,000

$12,000

Year 0 -$10,000

Year l Year 2 $2000 $2000

$4000

$8000

D)

Year 3 Year 4 $2000 $2000

Year 5 $2000

Yea r 6 $2000

Hint : (No calculation is necessary, a visual analysis of the years and the amount will give you the answer. Remember lending is a cash outflow and this is negative. Getting repayment is an inflow and this will be positive)

Answer: D) 2. A tenant wants to lease a building for $48,000 per year. She signs a five-year

rental agreement that states that she will pay $24,000 every six months for the next five years. Which of the following is the timeline for her rental payments, assuming she makes the first payment immediately? A)

1 2 -24

Year

0

1/2

1

CF ($000)

-24

-24

-24

0

1/2

1

1

24

24

24

24

1

1 2 -24

2

2

-24

3 -24

1 2 -24

3

4 -24

1 2 -24

4

5 0

B)

Year CF ($000) 

1 2

1 2

2

2

24

24

1

1 2

3

3

24

24

1 2

4

4

24

24

5 24

C)

Year

0

CF ($000)

48

1 48

2 48

3 48

4 48

5 48

1 -48

2 -48

3 -48

4 -48

5 -48

D)

Year

0

CF ($000)

-48

Hint : (This is similar to Q1 but pay attention to the number of periods. How many periods do you have in 1 year? This will give you an idea about the answer)

Answer: A) 3. Samantha enters a rent-to-own agreement for living room furniture. She will pay $60 per

month for one year. Which of the following shows the timeline for her payments if the first payment is one month from now? A)

Month CFs ($)

0 0

1 -60

2 -60

3 -60

4 -60

5 -60

6 -60

7 -60

8 -60

9 -60

10 -60

11 -60

12 -60

Month CFs($)

0 -60

1 -60

2 -60

3 -60

4 -60

5 -60

6 -60

7 -60

8 -60

9 -60

10 -60

11 -60

12 -60

4 -300

5 6 -360 -480

7 -540

8 -600

9 -660

10 -720

11 -780

12 -840

B)

C) CFs ($)

0 -60

1 -120

Month CFs

1 -$60

2 -$60

Month

2 3 -180 -240

D) 3 -$60

4 -$60

5 -$60

6 -$60

7 -$60

8 -$60

9 -$60

10 -$60

11 -$60

12 -$60

Hint : (Is this an annuity due, normal annuity or deferred annuity? Remember an annuity is a sum of money being paid or received and that sum says the same through the whole question.)

Answer: A)

4. The timeline shown below best describes the cash flow of which of the following people?

Date 0 (years) -$3500 Cash Flow

1

2

3

4

$1000

$1000

$1000

$1000

A) Karen, who loans a friend $3500, and whose friend pays back the loan in four annual

installments of $1000 

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B) Joe, who puts down $3500 to buy a car, and then makes annual payments of $1000 C) Harry, who borrows $3500, and then receives an annual payment of $1000 D) Leo, who borrows $3500, and then pays back the loan in four annual payments of

$1000 Hint : (This is similar to the previous questions 1, 2 & 3. Pay attention to borrowing or lending. If you are borrowing the sign is positive as it is a cash inflow and if you are lending it is negative and a cash outflow)

Answer: A) 5. Why is it usually necessary to use the time value of money when performing a cost-benefit

analysis? A) For an investment project to be considered, costs must have a higher dollar value

from benefits. B) Although costs and benefits generally occur concurrently, the benefits will accrue

value over time, due to interest. C) In most investment projects costs are incurred up front but benefits are

provided in the future. D) For practical purposes, a dollar today may be considered to be equal to a dollar at

some future time. Hint : (This is a general question from a combination of week 3, 4 and 5. The key word is cost-benefit analysis. This not a question asking you if the statements are true or false)

Answer: C) 6. Owen expects to receive $20,000 at the beginning of next year from a trust fund. If a

bank loans money at an interest rate of 7.5%, how much money can he borrow from the bank on the basis of this information? · A) $15,000 B) $21,500 C) $11,428 D) $18,605 Hint : (What is $20 000? Pay attention to the words “ expects to receive $20,000 at the end of next year”.We do have i, What is the question looking for PV or FV?)

Answer: D) 7.

An investment will pay $205,000·in one year's time for an investment of $183,000 today. If the market interest rate is 8% over the same period, should this investment be made? A) Yes, because the investment will yield $7360 more than putting the money in a bank. B) No, because the investment will yield $6240 less than putting the money in a bank. C) Yes, because the investment will yield $4280 more than putting the money in a bank. D) Yes, because the investment will yield $2360 more than putting the money in a bank. Hint : (There are 2 opportunities here, the first one an investment where you are and the 2nd one is an investment in the market and any investment in the market will earn 8%. You need to compare those and decide where the 1st investment is worthwhile.)



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Answer: A) 8.

If$476 invested today yields $500 in one year's time, what is the discount factor? A) 1.05 B) 0.95 C) 1.50 D) 0.05 Hint : (You have PV and FV. Is the discount rate the same as discount factor? The discount factor is 1/ denominator)

Answer: B) 9.

You are scheduled to receive $10,000 in one year. An increase in the interest rate will have what effect on the present value of this cash flow? A) It will have no effect on the present value. B) It will cause the present value to fall. C) It will cause the present value to rise. D) The effect cannot be determined with the information provided. Hint : (What is $10000, FV or PV? Use the PV formulae, change i but keep FV to see what happens to PV)

Answer: B) 10. If the interest rate is 5%, the one-year discount factor is equal to

A) 0.952. B) 1.050. C) 0.050 D) 1.045 Hint : (You can use the hint from Q 8 to attempt this. The discount factor is 1/ denominator and the discount rate is just i)

Answer: A) 11. What is the present value (PV) of $100,000 received five years from now, assuming the

interest rate is 8% per year? A) $82,609.42 B) $68,058.32 C) $60,000.00 D) $73,502.99 Hint : (Draw your timeline. What is the question looking for? What is $10000, FV or PV? You have n and i)

Answer: B) 12. If $15,000 is invested at 10% per year, in approximately how many years will the

investment double? · A) 14.8 years 

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B) 7.3 years C) 8.4 years D) 10.6 years Hint : ($15000 is PV, How much is FV? “Pay attention to the word “double”. You have PV, I and FV and you need to find n) 13.

Answer: B) 14. Sara wants to have $500,000 in her savings account when she retires. How much must she

put in the account now, if the account pays a fixed interest rate of 8%, to ensure that she has $500,000 in 20 years' time? A) $180,884 B) $107,274 C) $144,616 D) $231,480 Hint : ($500000 is FV, what is being asked for? PV. You have FV, I and n?)

Answer: B) 15. Which of the following statements is

FALSE? A) A dollar today and a dollar in one year are not equivalent. B) The equivalent value of two cash flows at two different points in time is sometimes

referred to as the time value of money. C) Finding the present value (PV) and compounding are the same. D) If you want to compare or combine cash flows that occur at different points in time, you first need to convert the cash flows into the same units or move them to the same point in time. Answer: C) 16. Which of the following investments has a higher present value, assuming the same

(strictly positive) interest rate applies to both investments? Yea r 1 2 3 4

Investment X Investment Y $5,000 $11,000 $7,000 $9,000 $9,000 $7,000 $11,000 $5,000

A) Investment Y has a higher present value. B) Investment X and Investment Y have the same present value, since the total of the cash

flows is the same for both. C) Investment X has a higher present value. D) No comparison can be made-we need to know the interest rate to calculate the present

value. 

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Hint : (No interest is given here but try the question for Investment X (interest = 10%) for both Investment X & Y then try and interest = 5%. Is the result the same? You will see that irrelevant of the discount rate, one investment will have a higher or lower value.)

Answer: A) 17. An investment pays you $20,000 at the end of this year, and $10,000 at the end of each of

the four following years. What is the present value (PV) of this investment given that the interest rate is 4% per year? A) $58,614 B) $45,913 C) $54,134 D) $42,150 Hint : (Similar to question 16 but without a table, draw your timeline and substitute the input. There are 2 ways to answer this, either discount each cash flow or you can also use an annuity formulae. Which is more quicker?)

The solution to this question has also been explained in a video uploaded on Additional Resources on Moodle.

Answer: C) 18. A homeowner in Queensland has the opportunity to install a solar water heater in his

home for a cost of $2400. After installation the solar water heater will produce a small amount of hot water every day, forever, and will require no maintenance. How much must the homeowner save on water heating costs every year if this is to be a sound investment? (The interest rate is 9% per year.) A) $216 B) $248 C) $240 D) $262 Hint : (ThisissimilartoQ17.Drawyourtimeline,Whatis$2,400?PV.UseaformulaewhichhasPV,PMT andIbutnoFV.Thekeywordisforever(Perpetuity)).

Answer: A) 19. A perpetuity has a PV of $32,000. Ifthe interest rate is 10%, how much will the

perpetuity pay every year? A) $3200 B) $3100 C) $2909 D) $3520 Hint : (YouhavePVandi.Thequestionisaskingforperpetuity,Whyis“n”notgiven?Wellitisgiven anditisinfinity.Sousetheperpetuityformulaetofindtheanswer.Youcanalsouseanannuity formulaetogetacloseanswerbyusingnwhichwouldbelarge,let’ssay10000.)

Answer: A) 20. An annuity pays $10 per year for 50 years. What is the future value (FV) of this

annuity at the end of that 50 years, given that the discount rate is 5%? A) $845.25 B) $182.56 

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C) $525.00 D) $2093.48 Hint : (Youhaven,PMTandI,calculateFV?)

Answer: D) 21. You are saving money to buy a car. If you save $300 per month starting one month

from now at an interest rate of 4%, how much will you be able to spend on the car after saving for 4 years? A) $41,778.96 B) $15,287.27 C) $13,286.65 D) $15,587.88 Hint : (Is it an Ordinary annuity or Annuity due? Be careful with the compounded periods. In this case the number of periods and number of years are not the same. You have PMT, n and i. Is question asking for PV or FV?).

The solution to this question has also been explained in a video uploaded on Additional Resources on Moodle. Answer: D) 22. You are borrowing money to buy a car. If you can make payments of $300 per month

starting one month from now at an interest rate of 4%, how much will you be able to borrow for the car today if you finance the amount over four years? A) $15,587.88 B) $6,358.54 C) $13,067.62 D) $13,286.65 Hint : (Similar to Q 23 except for… Is it PV or FV this time? How much can you borrow now? The key word is “now”.)

Answer: D) 23. Dan buys a property for $250,000. He is offered a 20-year loan by the bank, at an

interest rate of 6% per year. What is the annual loan payment Dan must make? A) $21,796.14 B) $32,684.66 C) $64,486.34 D) $24,864.98 Hint : (You have PV, n and i? Is the question asking for FV or PMT? They key word is “annual payment”)

Answer: A) 24. A bank is negotiating a loan. The loan can either be paid off as a lump sum of $100,000 at

the end of five years, or as equal annual payments at the end of each of the next five years. If the interest rate on the loan is 10%, what annual payments should be made so that both forms of payment are equivalent? A) $16,380 B) $12,000 

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C) $19,588 D) $20,000 Hint : (You have 2 methods of paying off the loan and they must be compared to each other so that the PV of each are the same. There are 2 ways to attempt this question, you can use both PV of annuity formuale or FV of annuity formuale. Which one of these 2 is the quickest method? Why?)

Answer: A) 25. Faisal has $15,000 in his savings account and can save an additional $5000 per year.

If interest rates are 12%, how long will it take his savings to grow to $50,000? A) 3 years B) 4.25years C) 5 years D) 2.5 years Hint : (You can use log in the question or you can use your calculator. If you use log, you will have 2 parts which will eventually equate to $50000. The first part is just $15 000 and the 2nd part is PMT and you need to find n. The best way to attempt the question is to draw a timeline. If you use your calculator, you have PV, PMT,I and FV. Calculate n. Remember either PV and PMT or FV must be entered as a negative figure.

Answer: B) 26. If the one-year discount factor is equal to 0.90909, the interest must be equal to

A) 10.0%. B) 9.1%. C) 9.5%. D) 5.0%. Hint : (Similar to Q8 & Q10. You need to be able to identify the discount factor from the PV formulae. Look at the hint for Q 8 & Q10)

Answer: A) 27. Salvatore has the opportunity to invest in a scheme which will pay $5000 at the end of

each of the next 5 years. He must invest $10,000 at the start of the first year and an additional $10,000 at the end of the first year. What is the present value of this investment if the interest rate is 4%? A)-$1410.67 B) -$112.23 C) $2643.73 D) $1248.56 Hint : (Draw your timeline and substitute the values in the correct year. The question is asking for NPV. That means you have to calculate Cash inflow less cash outflow. You can use the cash flow function in your calculator or you can discount each year accordingly.)

The solution to this question has also been explained in a video uploaded on Additional Resources on Moodle. Answer: C) 

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28. A perpetuity will pay $1000 per year, starting five years after the perpetuity is purchased.

What is the present value (PV) of this perpetuity on the date that it is purchased, given that the interest rate is 4%? A) $34,604 B) $1,410 C) $21,370 D) $20582 Hint : (The question mentions perpetuity however it is more than just a perpetuity, it is a deferred perpetuity. Again draw your timeline. There are 2 steps to this question, hence you will have to use 2 equations)

The solution to this question has also been explained in a video uploaded on Additional Resources on Moodle. Answer: C) 29. A perpetuity will pay $1000 per year, starting five years after the perpetuity is purchased.

What is the future value (FV) of this perpetuity, given that the interest rate is 4%? A) $21,370 B) $20,582 C) $1410 D) There is no solution to this problem. Hint : (CalculatetheFVofaperpetuity?AtwhichyearareyoucalculatingtheFV?Dowehavea formulaeforFVofaperpetuity?)

Answer: D) 30. Since you were born, your grandparents have been depositing $100 into a savings

account every month. The account pays 4% interest annually. Immediately after your grandparents make the deposit on your 18th birthday, the amount of money in your savings account will be closest to: A) $11,941,266 B) $21,600 C) $30,774 D) $31,559 Hint : (Thisisanexampleofanannuity.Itisageneralannuity,onemonthafteryouwereborn,$100was deposited.FindnandusetheFVannuityformulae. 

Answer: D) 31. You are interested in purchasing a new car that costs $35,000. The dealership offers you a

special financing rate of 6% APR (0.5% per month) for 48 months. Assuming that you do not make a down payment on the car and you take the dealer's financing deal then your monthly car payments would be closest to: A) $822 B) $647 C) 842 D) $729 

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Hint : (You have PV, i and n, Find PMT. Careful with the i as in this case number of periods and number of years are different.)

Answer: A) 32. A rich donor gives a hospital $100,000 one year from today. Each year after that, the

hospital will receive a payment 5% larger than the previous payment with the last payment occurring in ten years' time. What is the present value (PV) of this donation, given that the interest rate is 9%? A) $585,987.27 B) $467,922.22 C) $779,843.27 D) $772,173.49 Hint : (This is a growing perpetuity. CF0 means cash flow in year 0. CF1 means cash flow in year 1.)

Answer: C) 33. You are thinking about investing in a mine that will produce $10,000 worth of ore in the

first year. As the ore closest to the surface is removed it will become more difficult to extract the ore. Therefore, the value of the ore that you mine will decline at a rate of 8% per year forever. If the appropriate interest rate is 6%, then the value of this mining operation is closest to: A) $71,429 B) $166,667 C) $500,000 D) This problem cannot be solved. Hint : (This is the inverse of Q32, instead of increasing every year, the value will decrease. However, you cannot use the formulae you have used in Q32 as we do not have n. It goes forever. This is a perpetuity, or more specifically a decreasing perpetuity.

Answer; A) 34. The cash flows for four ...