calculate return (a) if the bank compounds annually (n = 1) with a deposit $20,000 for 3 years at a rate of 8%
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Amount = P{1+r)^n\n= 20000{1+0.08)^3\n= 20000{1.08}^3\n= 20000{1.259712}\n=$25194.24\n\nInterest = 25194.24 -20000 = $5194.24
693280
In order to compute a precise answer, you need all of the following information:\n\nAmount of principle subject to interest (one penny)\nFrequency of Compounding\nInterest Rate\nand the formula for compound interest (more on this below)\n\nUnfortunately, the answer to your question at this point, would have to be: One penny after 30 days.\n\nHow did I get there?  Well I had to make some assumptions:\n\nFirst we derive the formula for compound interest:\n\nEnd of Period Balance = Beginning of Period Balance Principle + Interest\n\nInterest = Beginning of Period Balance (times) interest rate\n\nWith multiple compounds you have multiple calculations of interest and the interest is added to the balance each time so that the next calculation has interest computed on the new balance which includes the previous interest.\n\nWhether you are looking at multiple years or multiple compounds in a year, you initially have interest on the principle then you have interest on the principle and interest on the prior interest, which is the "compounding".\n\nIt's not very reasonable for me to assume the interest rate (which was not given in the question) is significantly higher than currently available interest rates in the marketplace.  The question suggests the scenario is saving money, not paying bills.  Current interest rates on savings are well below 5 percent per year (closer to one percent per year).  Ask your local bank what interest rate they'll pay you on a simple savings account.\n\nIf the interest rate were 12 percent per year, and you compounded monthly then you could express the interest rate per period as 0.12 / 12 = 0.01 or one percent per month.\n\nOne percent per month would be a sizeable amount on a sizeable purchase, but one percent on a penny is one one-hundredth of a penny - hardly noticiable and most likely lost in the calculations.\n\nIt gets worse when you compound daily in this case\n\nInt rate  = 0.12 / 365 = 0.00032876712328767123287671232876712\n\nThat's assuming 12 percent interest per year (too high to be a good assumption)...and the result of multipling that by a penny even once is too close to a penny to notice the difference.  Making the calculation a little easier, you can calculate the new balance after interest is paid by adding one to the interest rate resulting in the new balance (representing balance = 1 times amount subject to interest plus the interest)\n\n$0.01 times 1.00032876712328767123287671232876712\ntimes 1.00032876712328767123287671232876712\ntimes 1.00032876712328767123287671232876712\ntimes 1.00032876712328767123287671232876712\netc. for 30 multiplications would yield you\n\na balance of 1.0099101764966712808084001310017 pennies which is still to small to practically be anything but one penny.\n\nThe rule of 72 allows you to approximate how long it will take for an amount to double under compound interest.  divide 72 by the annual interest rate and the result is an approximation of the number of years.\n\n72% interest would double your money in one year\n12% interest would double your money in six years\n7.2% interest would double your money in ten years\n\nYou'd need to get approximately 72% x 12 interest rate (864% interest per year) to compound a penny into two pennies in a single month.\n\nI imagine that you'd like to re-ask with the missing details (interest rate) and set a higher starting value than an penny.  I've hunted down a calculator for your so you can do some what-iffing on your own.\n\n-EN-
195821
The answer to your question, It will compound to $315,012.50 dollars in 20 years.\nOne of the easy way to caculate compound, you can do it online at Moneychimp.com.  Click on the link below.\n\nhttp://www.moneychimp.com/calculator/compound_interest_calculator.htm
836682
Yr 1. 9000*.08= 720 + 9000\nYr 2. 9720*.08=777.60 +9720\nYr3. 10497.60*.08=839.81+10497.60\nYr 4. 11337.41*.08= 907 +11337.41\nYr 5. 12244.41*.08= 979.60 + 12244.41\nYr6. 13224.01*.08=1057.92+ 13224.01 = $14,281.93 total repaid\n5,281.93 total interest
672493
IRR=PV/(1+K)^n=0\n\nPV=Present Value of the Investment\nK=Rate of interest in\nn=number of years
1126484
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 ..
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the formula for compound interest yearly is\n\nA=P(1+r/n)^(rn)\n\nwhere\nA=final amount\nP=Initial amount\nr=rate in deciamals\nn=number of times coumponded yearly \nMontly=12,quartely=4,daily=365.....
157348
To simplify calculations, lets just use the formula for simple interest:\n\nI = 12i = Prt , where:\n\nI = yearly interest\ni = monthly interest\nP = amount to be saved\nr = yearly interest rate, in decimal form\nt = time, in this case, 1 year.\n\nSolution:\n\nI = 12i = Prt\n\n1440 = 12(120) = P(0.045)(1)\n\n1440 = 0.045P\n\n0.045P = 1440\n\nP  =  32,000.00\n\nTherefore, you will have to save around $ 32,000 (in the bank?)
574778
first, start with how much money you have, then find the rate, and the time\n\nfor example:\nI have $20,000, at a rate of 12% for 36 months. The interest would be $20,000 times .12 times 36.
166252
The effective, or true, annual rate of return. The APY is the rate actually earned or paid in one year, taking into account the effect of compounding. The APY is calculated by taking one plus the periodic rate and raising it to the number of periods in a year. For example, a 1% per month rate has an APY of 12.68% (1.01^12 -1).
171884
There is not enough information in your question to determine what it is you are trying to find out.\n\nDo you mean to get your $30 back? If it is a dividend of $3 once a year then you would get your money back after ten years.
844754
I = Prt, \nwhere  I = interest, P = principal, r = interest rate and t = number of years\nP = 770, r = 3% = .03 and t = 9\nI = 770(.03)(9)\nI = 207.90
897105
balance would be $84901.25
1148875
The *right* way to figure this out is to use an algebraic\nformula, but I think it's easier to visualize if you use a\nspreadsheet.\n\nIt's slightly difficult to present a table in Yahoo Answers\nbecause everything is jammed hard against the left\nmargin.  [I'm not sure why that's a feature.]  To help\nreduce the column misalignment, I displayed all of the\nnumbers with a constant width (ie. with leading zeros\nwhen necessary).  Bottom line is that you'd have\n$30344.87 at the end of eleven years.\n\nYear == years since start of account (in half year increments)\nRate == interest rate\nBalance == running balance of account\nInterest == interest payment for previous 6 months\n\n\nYear    Deposit     Rate   Balance  Interest\n\n00.00    820.00     0.000  00820.00   0000.00\n00.50    820.00     1.050  01681.00   0041.00\n01.00    820.00     1.050  02585.05   0084.05\n01.50    820.00     1.050  03534.30   0129.25\n02.00    820.00     1.050  04531.02   0176.72\n02.50    820.00     1.050  05577.57   0226.55\n03.00    820.00     1.050  06676.45   0278.88\n03.50    820.00     1.050  07830.27   0333.82\n04.00    820.00     1.050  09041.78   0391.51\n04.50    820.00     1.039  10214.41   0352.63\n05.00    820.00     1.039  11432.77   0398.36\n05.50    820.00     1.039  12698.65   0445.88\n06.00    820.00     1.039  14013.90   0495.25\n06.50    820.00     1.039  15380.44   0546.54\n07.00    820.00     1.039  16800.28   0599.84\n07.50    820.00     1.039  18275.49   0655.21\n08.00    820.00     1.039  19808.23   0712.74\n08.50    820.00     1.039  21400.76   0772.52\n09.00    820.00     1.039  23055.38   0834.63\n09.50    820.00     1.039  24774.54   0899.16\n10.00    820.00     1.039  26560.75   0966.21\n10.50    820.00     1.039  28416.62   1035.87\n11.00    820.00     1.039  30344.87   1108.25\n\nAdditional comment:\n\nOh man, I messed this up.  Thanks to "Mark Taranto"\nfor catching and correcting my mistake.  \n\nI took yet another look at this and want to\nwork through it carefully.  We appear to have\nas many different answers as there are people\nsubmitting solutions.\n\nOn day 1, Joanne put in $820, so that's her's balance.\n\nAfter 1/2 year, the bank would add half of 5% interest,\nwhich is 820*.025 = 20.50 and Joanne would add another \n$820.  So after six months, she would have:\n\n$820 + $20.50 + $820 = $1660.50\n\n\nAfter one year, the bank will again add half of 5% as\ninterest, which would be $1660.50 * 0.025 = $41.51.  \nThen Joanne would add $820, so the new total would be:\n\n$1660.50 + $41.51 + $820 = 2522.01\n\nContinuing this process in the spreadsheet, the\nfinal result after 11 years is:\n\n$23809.46\n\nThe corrected spreadsheet follows:\n\nYear  Deposit  Rate    Balance  Interest\n\n00.0  820.00  0.0000  00820.00  000.00 \n00.5  820.00  0.0250  01660.50  020.50\n01.0  820.00  0.0250  02522.01  041.51\n01.5  820.00  0.0250  03405.06  063.05\n02.0  820.00  0.0250  04310.19  085.13\n02.5  820.00  0.0250  05237.94  107.75\n03.0  820.00  0.0250  06188.89  130.95\n03.5  820.00  0.0250  07163.62  154.72\n04.0  820.00  0.0250  08162.71  179.09\n04.5  820.00  0.0250  09186.77  204.07\n05.0  820.00  0.0195  10185.92  179.14\n05.5  820.00  0.0195  11204.54  198.63\n06.0  820.00  0.0195  12243.03  218.49\n06.5  820.00  0.0195  13301.77  238.74\n07.0  820.00  0.0195  14381.15  259.38\n07.5  820.00  0.0195  15481.59  280.43\n08.0  820.00  0.0195  16603.48  301.89\n08.5  820.00  0.0195  17747.24  323.77\n09.0  820.00  0.0195  18913.31  346.07\n09.5  820.00  0.0195  20102.12  368.81\n10.0  820.00  0.0195  21314.12  391.99\n10.5  820.00  0.0195  22549.74  415.63\n11.0  820.00  0.0195  23809.46  439.72
742272
An Interest Rate of 5.000 % compounded Annually\nWith an Initial Amount of $ 4000.00 over an 8 year term:\n\nYr   Ending Balance\n1    4200.00\n2    4410.00\n3    4630.50\n4    4862.02\n5    5105.13\n6    5360.38\n7    5628.40\n8    5909.82\n\nFinal Savings Balance: $ 5909.82\nInitial Investment plus Monthly Contributions: $ 4000.00\nTotal Interest Earned: $ 1909.82\n\nThis should answer your specific question, however, please know that most banks compound interest daily in that scenario you would have earned $ 1967.13 for a total of $5967.13.\n\nHope this helps!
214693
The annual return would be (1 + MonthlyRate)^12 - 1 (where ^12 means to the 12th power).  Componding monthly.\n\nSo, if you had a 1.0% monthly return, that would be 12.683% annual return.
70181
I'm trying to do this like a basic math question, so forgive me if I do end up giving you the wrong answer. Firstly, I'm assuming that you're going to pay the deposit payment first right? Plus I hope that DP means deposit payment, because if I'm wrong you can just ignore what I typed below. I also assume that your 18% yearly interest would be divided into 12 months payment. Okay! We start!\nFirst, you minus the deposit payment of 144,000 out of the total price of 720,000, leaving you the balance of 576,000. This was already confirmed in your question. \nNext, you have to deduct the amount you pay for the first year, which is a total of 9,600 x 12 = 115,200. When you deduct 115,200 from 576,000, you get 460,800 left. With me so far? Okay, we'll move on...\nNow you have four years left to pay up, so basically you divide the balance of 460,800 between the four years. You'll get 115,200 per year. \nNow remember the 18% interest per year? You'll find that if you apply 18% interest per month, you'll get the same amount as calculated per year. So let's stick to calculating per month, shall we?\nRemember the 115,200 you have to pay each year? Now divide that amount by twelve (months) and then times the answer with 118%. Yes, 118%. \n(If you prefer using 18% and then adding that to the month's original payment, that's also fine. But it's the long way round)\nMeaning:\n(115,200 / 12 ) x (118 / 100) = 11328\nSo this means that you have to pay 11328 per month (interest already included)for the next four years. Got it?