initial sum=$9000,rate of interest=6.5, interest compounded 2 times a year, no of years for amount to double?
459426
For compound Interest.\nA = a*(1+p/n)^(y*n)\n\nA = Final amount\na = Original amount\np = interest percentage (in this case = 6.5/100)\nn = no of times calculated/year\ny = no of years\n\n18000 = 9000(1.0325)^2y\n2 = 1.0325^2y\n\ny = [Log(with base 1.0325) 2] / 2\n\nRemembered anohter thing to help...Change of base rule\n\nlogx(b) = loge(b) / loge(x)\n\nSo next step would be..\n\ny = [ln(2) / ln(1.0325)]/2\n  = 10.836\n~~ 11 yrs
743411
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.
216093
compounded anually would use the equation: A=P(1+ (rate))^(#number of years) where A is total amount, and P is the starting amount.\ncompounded quarterly would be A=P(1+(rate/4)^(4(# of years))\nA and P are the same as above. (and rate is in decimal form for both, so 6% would be 0.06)\nSo you could plug in numbers to determine the difference.\nex: start with $1,000 with a rate of 6% and 10 years\nanually: A=1,000(1+ 0.06)^(10)\nA= 1,000(1.06)^(10)\nA= 1,000(1.79)\nA= $1,790.85\n\nquarterly: A=1,000(1+(0.06/4)^(4(10))\nA=1,000(1.015)^(40)\nA=1,000(1.81)\nA= $1,814.02\n\nSo, coumpounded quarterly earns you more money.
1043639
Let Your Money be Y and My Money be Y+0.5\nY+(Y+0.5)=5\nY+Y+0.5=5\n2Y+0.5=5\n2Y=5-0.5\n2Y=4.5\nY=(4.5)/2\nY=2.25\nHence:\nYour Money = Y = P2.25\nMy Money = Y+0.5 = P2.25+0.5 = P2.75\nQED#
297329
one formula you can use is\n\nF = P(1 + i)^n\nwhere,\n\nF = future worth of the money\nP = present worth of the money\ni = interest rate\nn = number of years\n\nsince the future worth of the money will be twice of the present worth, then we can say that,\n\nF = 2P\n\nusing this in the formula you'll come up with,\n\n-> 2P = P(1 + i)^n  \n(divide the whole equation by P)\n-> 2 = (1 + i)^n \n(n is 20 years)\n-> 2 = (1 + i)^20\n(raising the whole equation by 1/20)\n-> 2^(1/20) = 1 + i\n-> 1.035264 = 1 + i\n-> i = 0.035264\n-> i = 3.5264%
875073
Problem 1: If a piece of real estate purchased for $75,000 in 1998 appreciates at the rate of 6% per year, then its value t years after the purchase will be f(t)=75,000(1.06^t). According to this model, by how much will the value of this piece of property increase between the years of 2005 and 2008? \n\nf=75000*1.06^3=89326.20\nincrease=89326.20-75000=$14,326.20\n\nProblem 2: The amount A in an account after t years of an initial principle P invested at an annual rate r compounded continuously is given by A=Pe^rt where r is expressed as a decimal. What is the amount in the account if $500 is invested for 10 years at the annual rate of 5% compounded continuously?\n\n500*e^.05*10=500*e^.5=$824.36\n\n\n\nProblem 3: Find the number log5(1/5). \n-1
255187
sn777 is correct\n750 x .0125= 9.375 (for one month)\n9.375 x 6= 56.25 (for 6 months interest)\nadd your principle to interest:\n750+56.25 =  806.25 total due\n\nGen, $4 in interest total?
458986
Based on the rule of 72 your asset will double in 11.1 years.  \nHere is how the rule of 72 works;\n\n\nThis teaches you how to determine the number of years it will take for your investment or debt to double in value.\n\nDivide the number 72 by the percentage rate you are paying on your debt, or earning on your investment. Here are two examples...\n\nYou borrowed $1,000 from your friend, who is charging you 6% interest. 72 divided by 6 is 12. That makes 12 the number of years it would take for your debt to your friend to double to $2,000 if you did not make any payments.\n\nYou have a savings account with $500 deposited in it. It earns 4% interest from the bank. 72 divided by 4 is 18. It will take 18 years for your $500 to double to $1,000 if you don't make any deposits.\n\nRemember: 72 divided by the Interest Percentage is the number of years it takes to double.\n\n\n\n\nFor a calculator that you can use to determine how long it will take to double your money based on interest rates check this out.....
798202
Interest = Principal X Rate\nRate = Interest / Principal\nRate = 275 / 2500 = .11 = 11%
894668
the equation for interest is I=p*r*t\n\nso plug in 400 for I, 5000 for P and 4 for T(time) in years:\n\n400=5000*r*4\n\nthen you just solve for R\n\n\nhope that helped
165316
So what if the rate in the 9th year is 5% and then the rate in the 15th year is 15% and all other 10%?\n\nUh oh......\n\nUse a spreadsheet program and you can investigate differences much more easily.
539778
If you're looking to find the present value of a single sum, that has accrued interest at a specific rate, the equation is:\n\nPV=amount / (1+i)^n\n\n\nEx: An amount of $350,000 with 12% interest for five periods(or years)\n\nPV=350,000 / (1+.12)^5\nPV=$198,599.39\nAn amount today of $350,000 that had been growing for 5 years at 12%, was $198,599.39 five years ago.
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-
1095361
First, I should not that the "yield" I have been reporting is the interest earned.  Add $10,000 for the total amount in the account at the end of the investment period.\n\nSecond, you wrote the formula incorrectly.  The formula for continuous compounding has to include the interest rate, so\nA = Pe^(rt)\n\nGiven the information from the previous question ($10,000 at 10% for 2 years), continuous compounding would yield $2,214.03.\n\nIf we know that the bank returned $15,000 on a $10,000 deposit at 10%, the length of time must have been 4.05 years.\n\nIn 6.93 years, a deposit will have doubled.\n\nI apologize for the delay on responding to these questions--I have been on vacation.
457588
Simple interest has its own formula\nFV = P(1+rt)\nwhere FV is the future value(in this case the amount due on the loan), P is the principle, r is the rate and t is the time(in years)\nP = 1780, r = .12 and t = 6/12 = .5\nFV = 1780(1+.12(.5)) = 1886.8\nFor compound interest, use the formula\nFV = P(1+i)^n\nP is the principle, i is the interest rate divided by the number of times it is compounded per year, and n is the number of times it is compounded (n is in terms of months, years or whatever the problem states.\nFor example:\nIf it is compounded monthly, then\ni = .12/12 (divide by 12 because there is 12 months in one year) and r = 6 months\nFV = 1780(1+.12/12)^6 = 1889.51\nIf it is compounded annually, then\ni = .12/1 (because it is compounded once a year) and n = 6/12 = 1/2 years\nFV = 1780(1+.12/1)^(1/2) = 1883.77
907239
Okay, I would figure this out one year at a time:\n\nThe first year, the account would have:\n\n1.08(2500 + x) = 2700 + 1.08x\n\nwith x equaling the end of the year deposits. I multiplied by 1.08 to get the amount after the 8% interest was added.\n\nThe second year would be the above amount plus another x and multiplied by 1.08 for the 8% interest:\n\n1.08((2700 + 1.08x) + x) = 2916 + 1.1664x + 1.08x\n\nThe third year would be this amount plus another x and multiplied by 1.08 for the 8% interest:\n\n1.08((2916 + 1.1664x + 1.08x) + x) = 1.08(2916 + 1.1664x + 1.08x) + 1.08 x\n\nThe above equation represents the amount in the savings account after 3 years. Set that equal to 10,000 and solve for x:\n\n1.08(2916 + 1.1664x + 1.08x) + 1.08 x = 10000\nx = 1953.94\n\nSo the couple will have to deposit $1953.94 at the end of each year.
384122
Choose x to stand for the amount invested at 10%.  The remaining amount would be 15,000 - x.  It's invested at 6%\n\nChange the percents to decimals, multiply them by their amounts, and add them up to get the total interest:\n\n.10(x) + .06(15000 - x) = 1260\n\nDistribute the .06: .10x + 900 - .06x = 1260\n\nCombine like terms: .04x + 900 = 1260\n\nSubtract 900 from both sides:  .04x = 360\n\nDivide both sides by .04: x = 9000\n\nFind the other number:  15000-9000=6000\n\nSo, $9000 at 10% and $6000 at 6%.\n\nHope that makes sense!