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Finance

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Apr 3, 2024

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Financial Math Practice Solutions for Weekly Topic 2, 3,4 &5 The following questions have been divided into Fundamental, Intermediate and Short-answer questions For the fundamental level questions, you should be able to attempt them on your own after your pre–class reading. The intermediate level questions are those that you should be able to attempt after your weekly tutorial session. Short-answer questions are slightly more challenging which assess your ability of applying the learned knowledge to solve questions that are more comprehensive. kjhniohopjp Fundamental Level 1. During the period 1990 to 2014, the average yield on 3-month U.S. Treasury bills was 3.04%, the average inflation rate was 2.64%, the average yield on 30-year Treasury bonds was 5.49%, and the average return on 30-year Aaa-rated corporate bonds was 6.35%. The real risk-free short-term interest rate is A) 0.40%. B) 2.13%. C) 2.97%. D) 4.76%. 2. You are considering an investment in a AAA-rated U.S. corporate bond but you are not sure what rate of interest it should pay. Assume that the risk-free rate of interest is 2.5%; inflation is expected to be 1.5%; the maturity risk premium is 2.5%; and, the default risk premium for AAA rated corporate bonds is 3.5%. What rate of interest should the U.S. corporate bond pay? A) 8.5% B) 6.0% C) 5.0% D)9% 3. You are considering an investment in a U.S. Treasury bond but you are not sure what rate of interest it should pay. Assume that the real risk-free rate of interest is 1.0%; inflation is expected to be 1.5%; the maturity risk premium is 2.5%; and, the default risk premium for AAA rated corporate bonds is 3.5%. What rate of interest should the U.S. Treasury bond pay? A) 8.5% B) 6.0% C) 5.0% D) 2.5% 4. You discover an antique in your attic that you purchased at an estate sale 10 years ago for $400. You auction it on eBay and receive $8,000 for your item. What annual rate of return did you earn? A. 20.00% B. 30.47% C. 34.93% D. 200.00% 5. wen 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 based on this information? 1
A. $15,000 B. $21,500 C. $11,428 D. $18,605 6. 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. 1. 7. 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 8. If you only earned interest on your initial investment, and not on previously earned interest, it would be called simple interest. A. True B. False 9. Which of the following investments has the highest effective annual return (EAR)? (Assume that all CDs are of equal risk.) A. a bank CD that pays 7.25 percent compounded semiannually B. a bank CD that pays 7.00 percent interest compounded daily C. a bank CD that pays 7.30 percent annually D. a bank CD that pays 7.10 percent compounded monthly 10. You believe in the power of compounding and decide to save $1 per day by avoiding the purchase of a soda. You deposit the $1 at the end of each day in a bank account that pays 8% interest compounded daily. You are going to take a trip in 20 years with the money you have accumulated. How much money will you have in 20 years, assuming 365 days per year? A. $7,500 B. $12,438 C. $22,456 D. $18,032 11. 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. 2
Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 $0 $2000 $2000 $2000 $2000 $2000 B. Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 -$10,000 $2000 $2000 $2000 $2000 $2000 C. Year 0 Year l Year 2 Year 3 Year 4 Year 5 Year 6 -$10,000 $2000 $4000 $6000 $8000 $10,000 $12,000 D. Year 0 Year l Year 2 Year 3 Year 4 Year 5 Year 6 -$10,000 $2000 $2000 $2000 $2000 $2000 $2000 12. 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. Year 0 1/2 1 1 1 2 2 2 1 2 3 3 1 2 4 4 1 2 5 CF ($000 ) -24 -24 -24 -24 -24 -24 -24 -24 -24 -24 0 B. Year 0 1/2 1 1 1 2 2 2 1 2 3 3 1 2 4 4 1 2 5 CF ($000 ) 24 24 24 24 24 24 24 24 24 24 24 C. Year 0 1 2 3 4 5 CF ($000) 48 48 48 48 48 48 D. Year 0 1 2 3 4 5 CF ($000) -48 -48 -48 -48 -48 -48 Topic 4 13. Samantha enters a rent-to-own agreement for living room furniture. She will pay $60 per month for one year. Which of the following shows the timeline for her payments if the 3
first payment is one month from now? A. Month 0 1 2 3 4 5 6 7 8 9 10 11 12 CFs ($) 0 -60 -60 -60 -60 -60 -60 -60 -60 -60 -60 -60 -60 B. Month 0 1 2 3 4 5 6 7 8 9 10 11 12 CFs($ ) -60 -60 -60 -60 -60 -60 -60 -60 -60 -60 -60 -60 -60 C. Month 0 1 2 3 4 5 6 7 8 9 10 11 12 CFs ($) -60 - 120 -180 -240 - 300 -360 -480 - 540 - 600 - 660 -720 -780 - 840 D. Month 1 2 3 4 5 6 7 8 9 10 11 12 CFs - $60 - $60 - $60 - $60 - $60 - $60 - $60 - $60 - $60 -$60 -$60 - $60 Topics 3 & 4 14. The timeline shown below best describes the cash flow of which of the following people? Date (years) 0 1 2 3 4 Cash Flows -$3500 $1000 $1000 $1000 $1000 A. Karen, who loans a friend $3500, and whose friend pays back the loan in four annual instalments of $1000 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 15. 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 16. 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 4
B. $15,287.27 C. $13,286.65 D. $15,587.88 17. 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 Topic 4 18. 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 19. What is the present value of an annuity of $4,000 received at the beginning of each year for the next eight years? The first payment will be received today, and the discount rate is 9% (round to the nearest $1). A. $24,132 B. $25,699 C. $35,712 D. $36,288 20. Your company has received a $50,000 loan from an industrial finance company. The annual payments are $6,202.70. If the company is paying 9 per cent interest per year, how many loan payments must the company make? A. 12 B. 19 C. 13 D. 15 21. 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 the following: A. $822 B. $647 C. 842 5
D. $729 22. 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 23. The required rate of return reflects the costs of funds needed to finance a project. A. True B. False 24. The cash flows for four projects are shown below, along with the cost of capital for these projects. If these projects are mutually exclusive, which one should be taken? A. Yea r 0 1 2 3 4 5 CF - 20,000 $6000 $6000 $6000 $6000 $6000 WACC 8% B. Yea r 0 1 2 3 4 5 CF -15,000 $4000 $4000 $4000 $4000 $4000 WACC 7% C. Yea r 0 1 2 3 4 5 CF -18,000 $5000 $5000 $5000 $5000 $5000 WACC 7.5% D. Year 0 1 2 3 4 5 CF -12,000 $4000 $4000 $4000 $4000 $4000 WACC 5% 25. An investor has the opportunity to invest in four new retail stores. The amount that can be invested in each store, along with the expected cash flow at the end of the first year, the growth rate of the concern, and the cost of capital, are shown for each case. It is 6
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