Question

please answer all of the following questions

1. Which following statement is true, assuming an interest rate of greater than 0%: a. The present value of a dollar to be received one year from today is ALWAYS worth less than one dollar. b. The present value of a dollar to be received one year from today is ALWAYS worth more than one dollar. c. The present value of a dollar to be received one year from today is ALWAYS equal to one dollar. d. The present value of a dollar to be received one year from today could be worth less than, equal to, worth more than one dollar, depending on the size of the interest rate. e. All of the answers listed above are incorrect. 2. Which one of the following investments provides the highest effective annual rate of return (i.e., which of the following investments is the BEST (i.e., the largest EAR), assuming an investor wants to earn the best return over an investing horizon of 10 years)? An investment which has a 10.0 percent nominal rate with annual compounding. b. An investment which has a 9.85 percent nominal rate with semi-annual compounding. An investment which has a 9.75 percent nominal rate with quarterly compounding. d. An investment which has a 9.60 percent nominal rate with monthly compounding. An investment which has a 9.55 percent nominal rate and daily (365) compounding. a. с. е. 3. For a given nominal interest rate greater than 0 % , if the number of compounding periods per year decreases (for example, from quarterly to semiannually), the present value of $1000 to be received exactly 10 years from today will: increase. b. decrease. c. remain unchanged. d. either increase or decrease, depending on the nominal interest rate. a.

Answer 1

0 Let's just Interest rate= lol assume - A present value of $1= 1.1 ..tostod - = $0.909 .. present value of dollar to be received done year from today is always worth less than one dollar on t 230 option (a) is correct 2 Effective annual Interest rate CEAR) EAR= (1 + r) - where, & rate of Interest 12207 + 122 m = Compounting periods alas - now let's analyse all given four options using above formula Lero @ Y = 104 mar - EAR= [lt of] -1 2017 0 TI9 1 0.. 16 a 9.854. m=2 (semi-annual) EAR= [ 1+ - 098] ² ) 0.100926 - 10.09261

o r= 9.75% m=4 (quarterly Compounding) EAR= (1 + 0.09757 - 4 . 010112 3 82 16.1123.). r= 9.60% m= 12 (monthly Compounding) EAR= | lt 12 : (& 12 0.0960 (e) - 0.100339 - 10.0339). r=9.551. m= 365 (daily Compounding) E.A.R= (1+0.09557 363 - 1 365 E.A.R = .. 0.09557 11t . = 0.100195 10.0195%. gives highest loption & effective rate - 10.1234)

e ③ - Let's just assume Interest rate= 10% In case of Quarterly Compounding r=10/4 = 2.5% Present value of $1000 To be received after royears would be - love X c.o. = 1ooo x 0.37243.3 - $312-43 In Case If It decreases to semiannually - r= 10/2 = st. no. of periods = 10x2 = 20 present value after so years .: - 1000 x 1000% cros) 20 - တယ်။ 1 800 x 0.31689 = hence the option 'a' $376.89 present value is Correct Increases

o calculation of using discount Investment of net rate present value @ 4% Discount (1) p. v factor cash flows 4ooo present - value 0.9615 3846 مع 2500 0.9246 231):5 بن 2 000 1178 0.8890 0.8548 کے 1500 1282.2 9217.1 Net present value= 9a17.7 (-) 7000 $2211.7 Investment -11 Yr Cashflows pr.factor @u% 100 0.9615 0.9246 2000 rms present value 961.5 1849.2 2667 3419.2 3000 4000 0.8890 0.8548 8896.7 Net present value= 8896.7 (-) Tooo $ 1896.7 Net present value of Inust is higher because of time value of money hence Harison should choose Investment @ C . option b is Gorrect