3530_W24_Midterm 1 Q

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3530 W24 - Midterm Tutorial Session - Questions 1. How much are you willing to pay for a perpetual monthly income growing at 0.75% per month and starting today at $1,000 if the interest rate is 10%? A) $960,000 B) $975,253 C) $1,200,480 D) $1,209,000 E) Infinity 2. The current balance in your RRSP account is $120,000 and you want to retire in 30 years with $1,500,000. If you save $8,000 annually at the end of each year, what interest rate do you need to earn in order to reach your goal? A) 6.54% B) 7.75% C) 8.12% D) 9.37% E) 9.44% 3. What is the effective annual rate on a deposit of $3,000 made eight years ago if the deposit is worth $4,453.52 today? The deposit pays interest semi-annually. A) 2.50% B) 5.00% C) 5.06% D) 10.12% E) 12.50% 4. The cash purchase cost of an Apple Mac Pro is $8,000. You can finance the purchase with 60 equal monthly installments at an APR of 6.0% starting one month from today. If after two years you want to sell the computer, what is the minimum price for which you can sell it so you can pay off balance remaining on the loan? A) $2,935.76 B) $5,064.24 C) $5,891.31 D) $4,000.00 E) $5,083.91

5. What is the true value of a stated "$1 million prize", if the prize is paid out in 50 payments of $20,000 per year and the first payment is made immediately? The interest rate is 6.5%, compounded annually. A) $294,490 B) $313,632 C) $426,991 D) $675,274 E) $689,100 6. Compute the present value of the following set of payments for two years: $300 each quarter for the first year and $600 each quarter for the second year. The effective annual rate is 6% and payments will begin at the end of the first quarter. A) $3,000.56 B) $3,340.77 C) $3,514.06 D) $3,854.02 E) $3,999.14 7. Which of the following strategies will allow real retirement spending to remain approximately equal, assuming savings of $1,000,000 invested at 8% annually, a 25-year time horizon, and a 4 percent expected annual inflation rate? A) Spend approximately $63,000 annually. B) Spend approximately $78,225 annually. C) Spend approximately $93,680 annually. D) Spend approximately $127,500 annually. 8. You want to buy small condo in Toronto that requires a $400,000 mortgage. You are a high risk borrowers so Royal Bank of Canada amortizes the mortgage over 20 years at a rate of 7.00% (APR compounded semi-annually) for a 5-year term with monthly payments. What is the principal owing on the mortgage after 5 years? A) 400,000.00 B) $345,756.09 C) $344,399.80 D) $200,000.00 E) $55,500.20

9. What is the rate of return for an investor who pays $1,054.47 for a three- year bond with a 7 percent coupon and sells the bond one year later for $1,037.19? Assume the investor can reinvest the coupons at a 9% APR with semi-annual compounding. The bond pays coupons semi-annually and has a face value of $1,000. A) 5.00 percent B) 5.15 percent C) 5.30 percent D) 8.43 percent 10. What is the present value of a four-payment annuity of $100 per year that begins three years from today if the discount rate is 9%? A) 272.66 B) 322.87 C) 250.16 D) 424.00 E) 178.25 11. Consider a $1,000 face value bond with a 7 percent annual coupon. There are 9 years remaining until maturity. What is the current yield on the bond assuming that the expected rate of return on the bond is 10 percent? A) 7.00% B) 8.46% C) 8.52% D) 10.00% 12. If you purchase a seven-year, zero-coupon bond for $400, how much could it be sold for three years later if interest rates have remained stable? A) $592.39 B) $675.23 C) $400.00 D) $657.14 E) $1,000.00

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13.Three years ago, Alex bought a 10-year, 4% coupon bond at a 5% discount and he sold the bond today. He had reinvested all the coupons received during the 3 years at an APR of 8%. The yield to maturity of the bond today is 6.0%, and the bond pays interest semi-annually. The face value of the bond is $1,000. What was the effective annual rate of return (EAR) on her investment? A) 2.39% B) 2.50% C) 2.55% D) 6.99% E) 13.98% 14. The following information of a callable bond which pays interest semi-annually is given: The coupon rate is 2.80% and the number of years to maturity is 15. The bond is callable at 110% of par value in 7 years. If the par value is $10,000 and the current price is $9200, what is the yield to call? A) 2.69% B) 2.50% C) 2.55% D) 5.38% E) 13.98% 15. Given a future value (greater than zero), which of the following will contribute to a lower present value: A) Less time periods B) More frequent discounting C) Lower discount factor D) both A & B E) both B & C 16. Which of the following statements concerning amortizing loans is/are true? A) A large portion of the early payments is used to reduce the loan value B) Part of each payment is used to pay interest and part is used to pay off the loan C) There will always be a small unpaid balance at the end of the loan period D) Both B& C are true E) All of the above statements are true

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