A project with a 3-year life has the following probability distributions for possible end-of-year cash flows in each of the next three years:\n\nYear 1             Year 2         Year 3      \nProb  Cash Flow   Prob  Cash Flow   Prob  Cash Fl\n0.30    $300    0.15    $100      0.25    $200\n0.40     500      0.35     200      0.75     800\n.30     700      0.35     600      0.15     900\n           \n    \nUsing an interest rate of 8 percent, find the expected present value of these uncertain cash flows.  (Hint: Find the expected cash flow in each year, then evaluate those cash flows.)
120369
discounting factors for an interest rate of 8% \nat the end of  year 1 - 100/108 or 1/1.08 = 0.9259\nat the end of  year 2 - 1/1.1664 = 0.8573\nat the end of  year 3 - 1/1.2597 = 0.7938\n\n1.08, 1.1664, 1.2579 compound amounts at the end of year 1,2,3\n\nExpected Cash Flows\n\nDiscounting Factor.. 0.9259\nYear 1 Cash Flow .....$300...$500...$700\nYear 1 Dis Cash Flow..$278...$463...$648\nDiscounting Factor..0.8573.\nYear 2 Cash Flow .....$100...$200...$600\nYear 2 Dis Cash Flow..$86....$172...$514\nDiscounting Factor....0.7938\nYear 3 Cash Flow .....$200...$800...$900\nYear 3 Dis Cash Flow..$159...$635...$714\n\nYear 1\nDisc Cash Flow (x)..278...463...648\nProb P(x)...........0.3....0.4...0.3\nx.P(x) {px}.........83.4--185.2--194.4\n\nExpected Cash Flow in the first year = Sum(px)= $463\n\nYou should be able to calculate the rest..\n\nhttp://www.futureaccountant.com/probability/\n\nhttp://www.schoolingkids.com/
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I will assume that the interest is simple and compounded annually, just to make the question easier.\n\nYou will reach $1million (US system) 97 years later, at the age of 115.  $1,035,358, actually.\n\nI used a simple formula with an Excel spreadsheet to figure this out.
183301
You can find the answer here.\n\nhttp://www.swlearning.com/finance/brigham/ffm10e/ffm10e.html\n\nGo to chapter 8 and it will explain how to solve.
315539
(future value/present value)^(1/time)\n\nSo using your example, (200,000/$100,000)^(1/5) or the fifth root of 2, which is 1.148698 or 14.8698%.\n\nTo use your example, 1.148698 x 1.148698 x 1.148698 x 1.148698 x 1.148698 =2\n\nJust be careful with your units of time.  If you had found the monthly rate, you could not multiply it by twelve to find the annual rate, you would take it to the twelth power.\n\nOne simpler method, that is approximately correct is the rule of 72.  You can estimate most rates by dividing 72/time.  In this case it would give you 14.4.  It comes in handy when you don't have a calculator on hand.  See the wikipedia article on why it works.
70422
In other words, you want to know how much is the stream of payments worth today in a lump sum.  This is a really simple calculator that can tell you what that stream of payments is worth as a lump sum.  \nhttp://www.deseretfirstcu.org/calc/pvannuity.asp\nThe two main variables are, what interest rate is the company using and how long is the stream of payments?  If the stream of payments was going to be for lifetime, you would have to know what age their actuarials came up with for their calculation.\n\nI hope this helps.  Good luck.
161981
straight line = 150,000 (200,000 * 1/12 *3 years)\ndouble-declining = 115,740.75 (1/12 * 200% = 16.66%)\n\n200,000*16.66% = 33,333.33\n166,666*16.66% = 27,777.77\n138,888*16.66% = 23,148.15\n\nAccumulated depreciation after 3 years = 84259.25\n200,000-84259.25=115,740.75\n\nAny more homework you need done, ha!
152128
Hi there again - just answered your other annuity question.\n\nI'm assuming you are accumulating it up to the END of year 5. \n\nI'm also assuming that by an ordinary annuity you mean one where the payments are made at the END of each year (so at times 1, 2, 3, 4, 5 in this case).\n\nFrom scratch you could calculate it as follows:\n\n300×1.07^4 + 300×1.07^3 + 300×1.07^2 + 300×1.07 + 300\n\nAs the first $300 is paid at time 1 (end of year 1) and accumulated 4 years to time 5. The 2nd $300 is paid at time 2 (end of year 2) and so is accumulated 3 years to time 5. And so on.\n\nThis gives a value of $1,725.22 (to the nearest cent).\n\nThe quicker way is to use the accumulated value of an annuity formula which (for $1 a year) is:\n\n[(1 + i)^n - 1]/ i\n\nSo (1.07^5 - 1)/ 0.07 = 5.750739...\n\nSo for $300 a year it is $300 × 5.750739... = $1,725.22\n\nThis formula is found in Actuarial Science courses. \n\nNote that it is less than your annuity due question as the payments are received later and so are invested later - hence less interest is received.
94488
In total the dude made 9000, which is not quite a lot to be honest for me. (I spend too much). Anyway!\n\nSay the amount he invested at 7% is X, this would naturally make the rest 9000-X, right? Good.\n\nSo hee is the math!\n\n0.07*X + 0.1(9000-X)=720 ....... clear! Now for simplicity, multiply all by 100 and you will get:\n\n7X + 10(9000-X) = 72000 ... and after distribution:\n7X + 90,000-10X = 72000\n-3X = 72,000-90,000 = -18,000  \nX = -18,000/-3= 6,000\n\nSo this is the amount he invested at 7% and the rest, as we shwed earlier, is 9,000-X = 9,000-6000 = 3,000\n\nSo he invested $3,000 at 10%.\n\nOf course you know this is true if the interest was made in one year and without talking taxes, which would be anouther story.
336291
may be this will work,\n\nLets say all the years are 365 days each (skiping leap yrs for now)\nassume interest on daily basis.\n\nFor Nth dollar the interest would be;\n\n1+(An*7/100)\n\nwhere A is time left in years, and that would be,\nAn = (3650-n)/365\n\nyour series will start from 0 to 3649.\n\nnow on expanding (3650-n) we find that it turns out to be a simple arithmetic progression,\n\n3650, 3649.....2, 1 with n= 3650\n\nSimplifying we get \n\nTotal Amount = 3650*1 + ( 7/365*100 * sum of the above progression)\n\nusing arithmetic progression formula I get sum (n) = 3650*3649/2\n\nPutting all of it together,\n\nTotal Amount = 3650 + ( 7/365*100 * 3650*3649/2)\n\n= 3650 + 1277.15 \n= 4927.15
319370
1.  The expected value should be calculated likme this.\n\n(1/34 * 91) + (33/34 * 9) = 2.68 + 8.74 = 11.42\n\n2.  (37,000 * .7) - (18,000 * .3) = 25900 - 5400 = 20500
250711
The answer is D = 12%.\n\nThe way to do the math is with the following assumptions:\n\nPresent value = 404 (given)\nFuture value = 1,000 (par)\nPayment = 0 (zero coupon bond)\nNumber of time periods = 8 (given)\n\nSolve for the interest rate.\n\nThe way to check your answer is simply to use the equation:\n404 * (1.12) ^ 8 = $1000 so we know that 12% is correct!
640152
COMPOUND INTEREST\n---------------------------------\n\n S = P (1 + I) n \n\nwhere:\n\nS = the future value\n\nP = the principal amount\n\nI = the periodic rate of interest*\n\nn = the # of compounding periods for the term of the loan\n--------\n\nFor example,\n\nIf the principal amount is $10,000, the periodic rate of interest is 10% and the # of compounding periods is 6, what is the value at maturity?\n\nS = P (1 + I) n \n\nS = $10000 (1 + .10) 6\n\nS = $ 17715.61\n\nhttp://homepages.cambrianc.on.ca/tutorial/thetutorialcentre/mathscience/math/compound_interest.htm\n\n\nSIMPLE INTEREST \n------------------------------\n\nAt start:\n\nT = P\n\nAfter 1 period:\n\nT = P + Pr = P(1 + 1r)\n\nAfter 2 periods:\n\nT = P + Pr + Pr = P + 2Pr = P(1 + 2r)\n\nAfter 3 periods:\n\nT = P + Pr + Pr + Pr = P + 3Pr = P(1 + 3r)\n\nAfter n periods:\n\nT = P(1 + nr)\n\n--------------------\nWhen money is borrowed, interest is charged for the use of that money for a certain period of time. When the money is paid back, the principal (amount of money that was borrowed) and the interest is paid back. The amount to interest depends on the interest rate, the amount of money borrowed (principal) and the length of time that the money is borrowed. \nThe formula for finding simple interest is: Interest = Principal * Rate * Time. If $100 was borrowed for 2 years at a 10% interest rate, the interest would be $100*10/100*2 = $20. The total amount that would be due would be $100+$20=$120. \n\nSimple interest is generally charged for borrowing money for short periods of time. Compound interest is similar but the total amount due at the end of each period is calculated and further interest is charged against both the original principal but also the interest that was earned during that period. \nhttp://www.learningwave.com/lwonline/percent/interest.html\n\n\n\nhttp://www.aaamath.com/g84-simple-interest.html \na calculater ..
392184
Assuming you start at the beginning of a month\n\nFirst investment = $350\nAfter the 1st half month amount saved =  $(350(1 + r) + 350)\nAfter 2nd half month amount saved = $((350(1 + r) + 350)(1 + r) + 350)\n=$(350(1 + r)² + 350(1 + r) + 350)\nAfter 3rd half month amount = $350((1 + r)² + (1 + r) + 1)(1 + r) + 350)\n= $350((1 + r)³ + (1 + r)² + (1 + r) + 1)\nThat will mean that, at maturity,\nAmount = $350((1 + r)^20 + ...  + (1 + r)³ + (1 + r)² + (1 + r) + 1)\n= $350 ((1 + r)^21 - 1)/((1 + r) - 1)\n= $100000\nSo [(1 + r)^21 - 1] / r = 100000/350\nSo r/[(1 + r)^21 - 1] = 0.0035\nUsing Excel r = 0.2185\nie 21.85% per half year\nor 43.7% pa ... a rather ambitious interest rate!!\n\nAnd it would need to be high considering you are only investing 20 * $350 ie $7000 to mature at $100000 in 10 years
234081
I've found that the Wikipedia articles on probability distributions are top notch and contain enough information for you to solve this problem on your own.\n\nHint: solve the algebraic expressions that relate mean and variance so you can express p or n as algebraic relationship of one another and then do some substitions.\n\nAt first I thought you needed to know p or n up-front however I realize that you have all the info you need to solve this problem algebraically.\n\nGood luck with your homework.
594446
If each cash flow is subject to a binomial distribution (i.e. 60000 w/ a prob of 90%, and $0 otherwise) the the expected cash flow vector is the dot product of the $$$ & the probability vector.\n\nAssuming the investor is risk averse, the certainty equivalent NPV is simply the NPV of the expected cash flow vector discounted at the RFR.  The answer is b (w/ some rounding- I got $18701).\n\nIf you can't assume the binomial distribution or risk aversion, then the answer is d.
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For the second part, use the formula\nFV = P(1+i)^n,\nwhere P = 2400, i = .055, n = 4 and you are looking for FV\nFV = 2400(1+.055)^4 = 2973.18\n\nFor the first part:\nIs it compounded annually?  If so, then you will owe\n6000(1+.12)^6/12) = 6349.80
458101
Hi April,\nTaking what you know you have some amount invested at 5% (or.05) and the remainder of 30,000 invested at 9% (or .09). Since the first amount is unknown, we will call it X. Once we invest that we have the remainder to invest at 9%. \n\nLet X= amout invested @ 5%\n30,000 - X = amount invested @ 9%\n.05X + .09(30,000 - X) = 1940\n.05X - .09X + 2,700 = 1940\n-.04X = -760\nX=$19,000 \n\n$19,000 @ 5%\n$11,000 @ 9%\n\nOR\n\nLet X = amount invested @ 9%\nSo, 30,000 - X = amount invested @ 5%\n\n X(.09)  + ((30000 - X)*.05) = 1,940\n.09X - .05X + 1,500  = 1,940\n.04X = 440\nX= 11,000\n\n$11,000 @ 9%\n$19,000 @ 5%\n\n\nConfirms\n\nYou may further confirm:\n($11,000)(.09) + ($19,000)(.05)\n=$990 + $950 = $1,940!\n\nHave fun with your math :-)