Practice+Midterm+2+-+version+3

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1 Practice Midterm 2 Exam – Version 3 1. Anne makes semi-annual deposits into a fund earning interest at j 2 = 4%. Her first deposit is $200 and each succeeding deposit is 3% lower than the preceding deposit. What is the accumulated value of her fund immediately after her 20 th deposit? (A) $3694.72 (B) $3655.55 (C) $3768.61 (D) $3843.98 2. Deposits of $500 are made at the beginning of each month for 5 years at j 1 = 9%. What is the accumulated value at the end of 5 years? (A) $37,366.43 ( B) $37,712.07 (C) $37,635.75 (D) $37,994.91 3. Payments of $1000 are made at the end of each month in an account paying j 4 = 10 % . How much money will be accumulated in the account at the end of 4 years, if simple interest is paid for the fractional part of a period? (A) $58,722.49 (B) $59,109.69 (C) $58,622.52 (D ) $58,625.18 4. A deposit of $300 is made today into an account paying interest at j 4 = 5%. Deposits continue every 3-months, with each succeeding deposit being $10 higher. How much has been accumulated in the account just before the 16 th deposit is made? (Given: ° ±² | ³³³³³³ ´.´±µ² = 16.3863 ; ° ±¶ | ³³³³³³ ´.´±µ² = 17.5912 ) (A) $6550.32 (B) $6100.24 (C) $6632.20 (D) $6024.93 5. A research grant of $1,000,000 is given to a university by a donor. The university invests the grant in a saving account that pay · ±µ = 6% for the first 10 years and j 12 = 4.2% thereafter. The university decides to withdraw $ R every month forever, first withdrawal one month from today. What is R ? (A) $4046.76 ( B) $3597.91 (C) $2661.08 (D) $3447.40 6. Fund I is a perpetuity-due that pays $1000 every 6 months forever. Fund II is an ordinary perpetuity with semi-annual payments that start at $100 and increase by $ Q every 6 months forever. The present values of both funds are equal when j 2 = 8%. What is Q ? (A) $37.60 (B) $44.00 (C) $36.00 (D) $45.60 7. A 120,000 condominium (home) is financed with a down payment of $50,000 and a $70,000 mortgage from a lender. The mortgage has an interest rate of j 2 = 8% and a monthly payment of $534.25. What is the borrower’s equity in the house at the end of 5 years? (nearest dollar) (A) $55,505 (B) $59,877 (C) $64,495 (D) $60,123

2 8. Jim borrows $80,000 at j 12 = 12%, to be paid back with monthly payments over 15 years. After 3 years of payments, the outstanding balance is $73,102.10 and interest rates have dropped to j 12 = 9%. If he refinances the loan at this lower rate, he will be charged a penalty of 3 times one month’s interest on the outstanding balance. Taking into account the penalty, and assuming the loan is still to be paid back in full after 15 years, what will Jim’s new monthly payment be if he refinances the loan? (Given: 01 . 0 | 144 a = 76.1372 , 0075 . 144 a = 87.8711) (A) $850.64 (B) $856.88 (C) $981.74 (D) $ 988.94 9. A $15,000 loan is to be paid back over 10 years with semi-annual payments of $1153.14. The loan interest rate is j 2 = 9%. The total amount of interest owed over the life of the loan is $8062.83. What is the outstanding balance of the loan just after the 13 th payment is made using the sum-of-digits method? (A) $6996.97 (B) $7265.73 (C) $7842.95 (D) $9225.12 10. A loan of $5000 is taken out today and is repaid with monthly payments of $100 for as long as necessary. This is a loan with a “no payments for 6-months” deal, which means the first payment of $100 is not due until exactly 6-months after the date the loan. If the interest rate on the loan is j 12 = 6%, what is the loan outstanding balance at the end of 12 months (from the date the loan was taken out), immediately after the $100 payment on that day? (A) $4467.06 (B) $4700.84 (C) $4074.83 (D) $4597.80 11. A business borrows 2,000,000 at j 4 = 6% and they plan to pay off this loan over 10-years using the sinking fund method. Both the loan interest payment and sinking fund deposits are made quarterly. The sinking fund interest rate is j 4 = 4%. What is the book value of the loan after 6 years? (answer to the nearest dollar) (A) $944,734 (B) $986,300 (C) $896,483 (D) $824,156 12. A loan, A , is amortized with 25 annual payments of R . The principal portion of the 16 th payment is $609.35. The interest rate on the loan is j 1 = 2.5%. What is the value of A ? (answer to the nearest dollar) (A) $14,371 (B) $7,752 (C) $14,021 (D) $11,227 13. A $50,000 loan is taken out at j 2 = 4%. It is to be paid back with semi-annual payments of $3057.84 for 10 years. Using the sum-of-digits method, what is the amount of principal repaid in the 15 th payment? (A) $2,799.20 (B) $2,739.07 (C) $2,715.27 (D) $2,845.33

3 14. A loan of A is to be amortized over 20 years. The scheduled annual payments are as follows: $800 at the end of each year for 12 years, and $1000 at the end of each year for the next 8 years. The loan interest rate is j 1 = 5%. What is the interest portion of the 13 th payment? (A) $676.84 (B) $289.31 (C) $323.16 (D) $258.53 15. A $100,000 loan is amortized by means of monthly payments for 5 years. The loan interest rate is j 12 = 4.8%. Immediately after the 36 th payment there is an outstanding balance of $42,893.78. You wish to refinance the loan at that time at a new interest rate of j 12 = 2.4%. However, if you refinance you will be charged a penalty that is determined using the interest rate differential method (IRD). What is the amount of the penalty? (A) $514.73 (B) $3088.35 (C) $1029.45 (D) $2058.91 16. A company issues a $100,000 10-year bond paying interest at j 2 = 4%. The bond is redeemable at 102. The bond issue carries a sinking fund provision requiring the company to make semi-annual deposits into a sinking fund to accumulate to the redemption value by the end of 10 years. The sinking fund earns interest at j 2 = 3%. What is the company’s semi- annual expense? (A) $6411.07 (B) $6324.57 (C) $6451.07 (D) $5911.07 17. A loan is being repaid with n semi-annual payments of $1553.53. The interest portion of the 3 rd payment is $864.49 and the interest portion of the 6 th payment is $764.50. The loan interest rate is j 2 = x %. What is the value of x ? (A) Less than 8% (B) 8% or more but less than 8.5% (C) 8.5% or more but less than 9% (D) 9% or more 18. An n -year $100 bond is redeemable at 102 and pays semi-annual coupons at j 2 = 5%. It is purchased to yield j 2 = 5%. Which of the following statements is correct? (A) The bond is purchased at a premium (B) The bond is purchased at a discount (C) The bond is neither at a discount nor at a premium (D) We cannot tell if the bond is purchased at a premium or a discount without knowing the the term of the bond. 19. A 10-year $5000 bond is purchased for $5240.70 to yield j 2 = 7.8%. The bond pays semi- annual coupons at j 2 = 8%. At what rate is this bond redeemable at? (You are given: ¸ µ´| ³³³³³ ´.´¹º = 13.7115 , ¸ µ´| ³³³³³ ´.´» = 13.5903 ) (A) 103.4 (B) 113.5 (C) 107.4 (D) 109.5

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4 20. You buy a 10-year accumulation bond (compound interest bond) with a face value of $10,000, redeemable at 103, paying interest at j 2 = 7%. If the desired yield rate is j 2 = 6%, what price would you pay for this bond? (A) $10,909.98 (B) $11,106.98 (C) $10,166.10 (D) $11,183.08 21. A $5000 bond pays semi-annual coupons of $225 every August 13 and February 13. Alice buys this bond on August 13, 2015 (just after the coupon is paid that day) for a quoted price of q = 104. She sells the bond on February 13, 2020 (after receiving the coupon that day) for a quoted price of q = 98. Using the method of averages, what yield rate, j 2 , did Alice earn over the time she owned the bond? (A) 7.59% (B) 10.23% (C) 7.72% (D) 10.10% 22. A $1000 bond with semi-annual coupons is redeemable for $1030 in 5 years. The absolute value of the write down (book value adjustment) in the first coupon is $3.99 and the absolute value of the write down (book value adjustment) in the 5th coupon is $4.85. What is the price of the bond? (A) $1050.19 (B) $949.81 (C) $1080.19 (D) $979.81 23. A $1000 bond that pays interest at j 2 = 11% is redeemable at par on November 29, 2022. It is purchased on October 5, 2019 at market price of $1141.59 to yield j 2 = 6%. What is the actual price paid for the bond on October 5, 2019? (A) $1103.03 (B) $1125.15 (C) $1158.03 (D) $1180.15 24. A par value bond pays semi-annual coupons of $100. It is bought to yield j 2 = 5%. The book value adjustment at the end of 10 years is ̶ $22.09. What is the price of the bond? (A) $4552.80 (B) $3292.40 (C) $4707.52 (D) $3447.20 25. A $1000 callable bond pays semi-annual coupons at j 2 = 8% and is redeemable at par in 10- years. It is callable at 105 as early as the end of 5-years. What is the maximum price the buyer of the bond would be willing to pay if the desired yield is j 2 = 7%? (A) $1041.58 (B) $1071.06 (C) $1027.03 (D) $1077.03 26. The XYZ corporation buys a 20-year bond with a face value of $100,000. The bond pays semi-annual coupons of $2875 and is redeemable at 104.5. They keep the first 4-years of coupons, but sell the last 16 years of coupons to investor A who wishes to yield j 2 = 5% and sell the strip bond to investor B who wishes to yield j 2 = 5.50%. What is the total price paid by investors A and B to the XYZ corporation? (A) $85,341.55 (B) $98,121.95 (C) $86,861.89 (D) $96,601.61

5 27. Let i be the cost of capital and IRR be the internal rate of return for an investment. Which of the following statements are true in cases where there is a unique IRR? (NPV = net present value) (I) If i < IRR, then NPV > 0 and the investment should be undertaken/proceed (II) If NPV = 0, then i = IRR = 0 (III) If i > IRR , then NPV < 0 but the investment should still be undertaken/proceed (A) (I) only (B) (I) and (III) (C) (I) and (II) (D) (II) only 28. A machine costs $500,000 and produces 5000 items per year. It has a useful life of 15 years, after which it can be sold for $40,000. Maintenance costs are $ M per year. If the cost of capital is j 1 = 8%, the capitalized cost of the machine per unit of output is $154.85. What is the value of M ? (A) Less than $4000 (B) At least $4000, but less than $4500 (C) At least $4500, but less than $5000 (D) At least $5000 29. A company is considering financing a certain project that has the following estimated cash flows: Year End 0 1 2 3 4 Cash Flow ̶ 65,000 ̶ 35,000 0 60,000 90,000 If the company’s cost of capital is 9% and it believes they can earn 7% on any reinvested cash flow, what is the modified internal rate of return? (A) 9.09% (B) 12.25% (C) 23.93% (D) 29.39% 30. A machine company has office equipment costing $10,000. The book value of the equipment after two years, using the constant percentage method of depreciation, is $8000. What is the total (cumulative) depreciation at the end of four years? (Answer to the nearest dollar) (A) $3600 (B) $755 (C) $5904 (D) $6400 31. A machine costs $20,000 and has an estimated lifetime of 12 years after which it could be sold for $3000. Annual maintenance costs are $1500. If the cost of capital is j 1 = 6%, what is the annualized cost (periodic cost) of this machine? (Answer to the nearest dollar). (A) $61,800 (B) $64,777 (C) $3,708 (D) $3,886

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