Mock Exam. MBF3C: Mathematics of Personal Finance. Duration 3 hours. Non-Programmable calculator allowed

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Mock Exam MBF3C: Mathematics of Personal Finance Duration 3 hours Non-Programmable calculator allowed Answer all questions on the question paper Use blank side of the sheets for rough work, if needed.

1 Mock Exam MBF3C: Mathematics of Personal Finance Duration 3 hours Non-Programmable calculator allowed Answer all questions on the question paper Use blank side of the sheets for rough work, if needed. Name: Date : Section Your score Total Marks Knowledge 25 Communication 25 Problem solving 25 Application 25 Total 100 Good Luck! Knowledge For the questions below, please circle correct answer. 1. Simplify the expression. Use positive exponents. Assume variables represent non-negative numbers. (-4a 4 ) 4 (a) 16a 4

2 2 (b) (-4) 16 a 16 (c) (-4) 16 a 4 (d) (-4) 4 a 16 (e) (-4) 4 a If x and y are non-negative, simplify ( 256x y ) (a) 4xy (b) 4x y (c) 4x y * (d) 16x y (e) none of the above 17x 3. Solve 1 = 0 x + 6 (a) (b) 8 3 * (c) 8 (d) 16 1 (e) none of the above 4. Which of the following represents three arithmetic means between 7 and 23? (a) 13, 14, 15 (b) 9, 15, 21 (c) 12, 15, 18 (d) 11, 15, 19 * n! 5. Which of the following is the simplification of? 2 ( n 2! n (a) 2( n 1) n 1 (b) 2 1 (c) - 4 (d) (n-1)!

3 3 n( n 1) (e) * Find the sum of the series: (a) * 3 64 (b) 3 28 (c) 3 24 (d) 9 (e) none of the above 7. Find the 18 th term of the sequences where a =3 and d=7. 1 (a) 129 (b) 136 (c) 119 (d) 122 * (e) The n th term of the geometric sequence 3,-6,12,-21 is (a) a n = 3(-2) n-1 (b) a n = 2(-3) n-1 (c) a n = 2(3) n-1 (d) a n = 3(-2) n (e) a n = 3(2) n-1 9. What statement is true? (a) Canada Savings Bonds are guaranteed and are cashable at any time (b) Common stocks are guaranteed and are cashable at any time (c) Blue-chip stocks are a high-risk investment. (d) Mutual funds are a pool of investors money in bonds. (e) None of the above 10. Solve for x: 2 3x-1 = 4 x+5 The value of x is: (a) 4/3 (b) 3 (c) 11 (d) none of the above 11. Which of the following is related to an arithmetic sequence? (a) linear growth (b) simple interest (c) constant rate of change

4 4 (d) all of the above 12. Which of the following statements is true? (a) Purchasing a new car usually has a higher overall cost in the long run than leasing the same car (b) At the end of the lease period you will own the car. (c) Leasing rates usually depend on the expected number of kilometers of usage over the lease period (d) The monthly payments for a lease are usually higher than monthly payments for a new car loan. 13. Which of the following is an example of exponential growth? (a) a salary that increases $1000 every year (b) an investment that grows at the rate of 7% compounded semi-annually (c) the number of hours of daylight each day of the year (d) the height of a homerun baseball 14. Christina calculates the following expression to determine the present value of an annuity: 350 [1- ( ) -16 ] The present value of the annuity is: (a) negative (b) between $0 and $4000 (c) between $4000 and $10000 (d) over $ Which statement is true? (a) y=3x is linear and y=3 x is quadratic (b) y = 6x+7 is linear and y = x 2 is exponential (c) y = 4x is linear and y = 4 x is exponential (d) y = 2 x is quadratic and y =x 2 is exponential 16. Describe the steps you would follow to find the term required for $50,000 to grow to $75,000 at 8%, compounded semi-annually? (4 marks) 17. How do annuities relate to geometric series? How about arithmetic series? (5 marks)

5 5 Communication Answer the following questions in the space provided. 18. Complete the following 4 questions, each worth 3 marks (total 12 marks). (a) Describe three different types of investments (b) List some advantages and disadvantages of each. (c) Why might a person consider each of these types of investments. (d) Why might an investor combine investments? 19. A medical student is conducting an experiment. She treats a virus culture to a dosage of 256mg of a new drug to see how the virus responds. IN the next treatment, she uses ½ other dosage of the drug. In the next treatment, she uses ½ the dosage of the second treatment. This continues for a total of 7 treatments. How many milligrams of the drug will she need to conduct this experiment? (4 marks) 20. John is 25 and his goal is to retire at age 55. He has just started to pay $50 a month into a retirement investment that is expected to earn 8%, compounded monthly. He is considering these two options for increasing the future value of his retirement find: Option A: Double his monthly payment every 10 years, that is, at the age of 25, and then again at 45. Option B: Double his monthly payments right away.

6 6 Which option should he choose? Justify your advice to Peter using the appropriate calculations and terminology. (4 marks) 21. The value of a computer used in business can be depreciate at a rate of 30% each year. (a) Write an expression to model the decrease in value of a computer with initial value of $3,200 (2 marks) (b) Determine the valued of the computer after 2 years. (1 marks) (c) The company plans to replace the computer at the end of 5 years. The company offers the old computers to employees to buy for home use. Calculate the depreciated value of the computer at the end of 5 years. (2 marks) Problem solving Solve the following problems. Please show work. 22. Consider the equation 2 x = 10. How might you solve this equation. Explain. Fine the value of x, to one decimal place. (3 marks)

7 7 23. Create a sequence that is neither geometric nor arithmetic and explain why it is neither type of sequence. (4 marks) 24. Which do you think would save more interest? (3 marks) A: Pay off $2100 of a mortgage each year on their anniversary date. B: Pay an extra $175 at the end of each month. 25. For a vacation to England, the Elise s purchased 500 (British pounds) at an exchange rate of $2.298 per British pound. A week earlier, the exchange rate was $2.255 per British pound. How much extra, in Canadian dollars, did the Ellise's spend by waiting the extra week? (2 marks) Justify your answer. (Option B will save more interest, since interest on a Canadian mortgage is compounded semiannually) 26. In order to save $50,000 for the replacement of machinery, a company deposits $10,000 into a fund paying interest at 5%, compounded semi-annually. Equal deposits are then made into the fund every 6 months for 5 years. What is the amount of each deposit? [3 marks] $

8 8 27. The Cohen family owes $72, at 7.75% interest over a 10-year term. By changing their mortgage to a new lender, they will save $1500. If they will have to pay a 3-months interest penalty, should they switch to the new lender? Explain. (3 marks) Yes 28. Sarah invested $1250 at 4% compounded semi-annually, for 3 years. She then re-invested at 6%, compounded quarterly, for 5 more years. What will her investment be worth at the end of the 8 years? (4 marks) $ The intensity, or brightness of the light coming from an electric lamp can be calculated using the formula I=kD -2, where I is the intensity, in lumens (lm), D is the distance from the light, in meters and k is a constant that varies with the light source. (a) What happens to the intensity of light when the distance is doubled? (1 mark) (b) What happens to the intensity of the light when the distance is halved? (1 mark) (c) What happens to the intensity of the light if the constant is doubled, for a different light source? Explain. (1 mark) Application 30. Ben has saved $8000 to spend on a car. He needs a reliable car for getting to work, so, he decides to use his savings as the down-payment on a new car. He takes advantage of the year-end clearance to buy a vehicle for a total of $18,950, including all taxes and delivery charges. The dealership finances the balance at 2%, compounded monthly. Ben agrees to repay the loan in equal monthly payments over 3 years. How much will each monthly payment be? (3 marks)

9 9 31. A travel agency advises Monica to wait until the end of the month to purchase U.S. dollars for a trip to Florida. The exchange rate now is $ Cdn = $1 U.S. The travel agency predicts the rate will drop to $ by the end of the month. (a) if Monica takes the agency s advice, how much will she save on a purchase of $1000 US? (3 marks) (b) List 3 ways Monica could research the current exchange rate for U.S. dollars. (3 marks) 32. John and Jill each purchased half of a semi-detached home. Each of them has the same mortgage of $105,000 at 10.25%. John chose a 20-year amortization period, while Jill chose a 25-year amortization period. (a) What is the monthly payment for each person? (2 marks) (b) Who will pay less total interest over the life of the mortgage and by how much? (2 marks) 33. Frank s 20-year investment earned 23, in interest. The average annual simple interest rate was 7%. How much did he invest 20 years ago? (3 marks) 34. Sunnyside secondary school has a capacity of 1600 students. The school which is in a growing area of a city now has 1150 students. The school population is increasing at a rate of 5% per year. (a) Write an exponential function to model the growth of the school s population. [2 marks] y= 1150(1.05) n, where y is the projected population and n is the number of years. (b) Use the model to predict the population in 2 years. [2 marks] 1268

10 10 (c) Using a graph, or another method, predict when the school population will be greater than its capacity. [2 marks] 7 years 35. Ida has $23,256 in an account that earns interest at 4%, compounded quarterly. What regular amount could she withdraw from her account at the end of each quarter, over the next 5 years? [3 marks] $ THE END-

Year 10 General Maths Unit 2

Year 10 General Maths Unit 2 Year 10 General Mathematics Unit 2 - Financial Arithmetic II Topic 2 Linear Growth and Decay In this area of study students cover mental, by- hand and technology assisted computation with rational numbers,