MA 373 F11 Solutions to Quizzes

MA 373 F11 Solutions to Quizzes - Quiz 1 Math 373 September...

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Unformatted text preview: Quiz 1 Math 373 September 7, 2011 1. You are given that the nominal interest rate compounded quarterly ialculate the following accurate to 6 decimal places. a. Annual effective interest rate CM» n ‘\ 3" L” Ml?“ 1‘} b. Quarterly effective interest rate -(u) __ Q? m ’ 9’1? : L9? 2" a) ,0 Le (:3 (QC; .(‘/2. c. Monthly effective interest rate *5) 13%?” '51?) l% _ ‘flg \(u J - l“) cu L )ng a; L; i ,, fraf> \ (M3 \}3 / éwm‘eK WT wleoooL-W’b )2?!” ’ ‘ “(J/92w d a“) t; .M) 01> D" W a”) K / 4’ £2; )w 0%,) i” Q “E; ‘9 l“ ‘72; M «ad/e, 2. You are given: a. a(t)=1+ct+.0011‘3 where c is a constant b. 510 =0.14 Lexi invests 1000 at time 0. How much will she have at time 10? 5“ n ., “if: ~ I t5 C1 in 0.042 IQ /(3 3 + a 00:) mi anew/ma) @Mz’ee wigs? d: sag 02% we mm a: Wig :. @[%>$ W» 0.9%: “t 9'99”? j a}; Moat; wt; 3 mo (7+ WS’WWWW: st g2 gm 3. Emily invests 1000 at a simple rate of interest 5. Emily will earn an effective rate of interest of 5% in the 11th year of her investment. How much will Emily have at the end of 40 years? , a y (l/ / }+(n«i§5 Quiz 2 Math 373 September 20, 2011 1. Daniel loans Qian 15,000. Qian agrees to repay the loan with three annual payment. The first payment is 7000, the second payment is 6000, and the last payment is 5000. Daniel reinvests each loan repayment at an annual effective interest rate of 8%. a. Calculate the Qian’s annual rate of interest on the loan. me 2a; (200 55 z @000 £0; 3: W?Q¢9CD 5,02% W (QQQQ b. Using the bottom line approach, determine Daniel’s annual effective yield on this transaction. é mo 52; QC? i3 is; We 2. Kal|i invested 50,000 in an account three years ago. One year ago, the account had a balance of 120,000 and Kalli withdrew $50,000. Today, Kalli has 40,000 in the account. Determine the annual effective time weighted return earned by Kalli on this account. 5%” 1w) W43 @6906“; Q a Math 373 Quiz 3 October 5, 2011 1. An 15 year increasing annuity with payments made continuously pays at a rate of lOOOt at time t. Calculate the present value of this annuity at an annual effective interest rate of 6%. ,5?" 5; PM 2. Minsung is receiving an annuity that makes payments at the end of each quarter for 25 years. The payments are 10 during each quarter of the first year. The payments are 20 during each quarter of the second year and continue to increase 10 each year until 250 is paid each quarter of the 25th year. Calculate the present value of these payments at an interest rate of 8%. “ ~7492~§ . A 5-year continuous annuity makes payments at a rate of 2!2 at time t. Determine the present value of this annuity using a discount function of 1—0.021‘2. 2’ EM an {a a @‘J 3 % b Math 373 Quiz 4 October 18, 2011 1. A loan of 100,000 is being repaid using the sinking fund method over ten years. The sinking fund receives level annual payments such that the amount in the sinking fund after 10 years is just sufficient to repay the loan. The interest rate paid by the sinking fund is 8%. The total annual payment (interest and sinking fund deposit) made each year is 16,027.95. Determine the interest rate on the loan. 2. A loan is being repaid with level monthly payments of 250. The interest rate on the loan is 9% compounded monthly. The interest in the 10th payment is 44.14. Determine the interest in the 17th payment. f “1% p”? g: fifty/WM?“ , W} 44.1% “it PM M“ ?r@ “I; W 4,4,14qu “ET” gag” gb @fiemwae tr; W k WWMQ m a? 7 3. A loan is being repaid with annual payments over four years. The total interest paid on the loan is 1340.60 and the total principal paid on the loan is 12,000. Determine the annual effective interest rate on the loan. 707741; WVMMTS E” ,4?an «:3?E£ggf + 793mg ngfléffi’fi Math 373 Quiz 5 November 1, 2011 1. Wang LTD pays a quarterly dividend of 8. The next dividend is due later today. Calculate the price of the stock today (prior to the payment of the dividend) to produce an annual effective yield of 10%. 2. A preferred stock of pays its next dividend of 5 in 3 months. Each dividend thereafter is 1 larger than the previous dividend. in other words, a dividend of 5 is paid in 3 months, a dividend of 6 is paid in 6 months, a dividend of 7 is paid in 9 months, etc. Calculate the price ofthis stock to yield 8% convertible quarterly. K [p “’7 yy 2/14 3%? x ‘ \ 3. You are given the following spot interest rates: Calculate the price ofa 3 year bond which matures for 10,000 and pays annual coupons of 300. IIMMEII IIIEEII IIIEHII IIIIIII IIIEHII 1.0 1.5 IIEMHII 2.4 2.7 IIEMIII /QQQ@ 30$ 4. You are given the following spot interest rates: One year from now, Bill will receive a payment of 100,000. Bill intends to invest that payment 1.0 1.5 2.4 2.7 .0 for the following two year period. Using the above the spot interest rates and the implied forward interest rates, determine the expected value of this payment at the end of 3 years. H l l 3 %\/ Gage l9 / There are three exercise styles for options - American style, Bermuda style, and European style. ‘ Define each one. Amgi‘icm— flé’fl‘v Lg emrcispfliv {3mm 7’90 fare/flmv Km. 5M m 745;, . Elley enters into a short one year forward contract on the stock of Ma Company. The current stock price of the Ma Company is 100 and the forward price is 105. Complete the following table. Show your work. Spot Price at Expiration 3. Circle each of the following that are true. For each statement that is false, change the sentence to make it true. a. if the spot price at expiration on a put contact is greater than the exercise price, then the profit is zero. Your automobile insurance policy is a derivative. & was Jim e; A hurricane is a We risk. ‘59, d. The maximum profit on the sale of a call option is the WWW {Swim/re {pg Pram 51W 4. Jon purchased a stock at the current spot price of SO. One year later, Jon sold the stock for 200 for a profit of 50. The annual effective risk free interest rate is 8%. Determine SO. 7 U f; F: @032? WWW, {an} A 22:, mwvmg‘u‘zm szmyzximamméfwvr«r’7§’:‘wtmmm . g; 59 Math 373 Quiz 7 December 1, 2011 1. The current price of the stock of Moiitor Manufacturing Company is 48. The premium for a one year call with a strike price of K is 8.00. The premium for a one year put with a strike price of K is 9.53. The annual effective risk free interest rate is 6%. Determine K. Cl P2: @.§ £06m 2. You are given the current price of the stock of Actuarial Options LLC is 80. The stock does not pay a dividend. You are given the following premiums for one year options with various strike prices: Put Premium Strike Price Call Premium 70 18.38 3.19 l l l l 80 | 12.57 i 6.64 | 90 8.26 | 11.59 _j _ | The annual effective risk free interest rate is 8%. You enter into @n Actuarial Options. Determine the maximum gain and maximum loss (negative gain) that’Zu can have on this transaction. gt: be gT‘Qefi W{ jgkrfilhw a. (bail/l wafisw gig-3p? Q€$§.Q , , ’600bfi7 3. You are given the current price of the stock of Actuarial Options LLC is 80. The stock does not pay a dividend. You are given the following premiums for one year options with various strike prices: Strike Price | Call Premium | Put Premium W 70 l 18.38 | 3.19 80 12.57 6.64 The annual effective risk free interest rate is 8%. You purchase a straddle on the stock of Actuarial Options. Determine the payoff and profit on the straddle if the spot price of the stock is 100 at the end of one year. guy aver boil/k éivilée éfiaw 743 N ...
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MA 373 F11 Solutions to Quizzes - Quiz 1 Math 373 September...

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