Find the rate of interest compounded annually at which a sum of money will double in 20 years.
123690
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%
162180
For a 5% increase the growth factor is 1.05; for 8.75%, it's 1.0875; for 15%, 1.15.\n\n$30 at 4.5% compound interest (compounded how often?) for 2 years is 30*(1.045)^2 = 32.76
206266
You can get a rough but quick estimate by halving the time, calculating the sum+interest and dividing the result by number of quarters. That is x(1+10*0.076)*80=2000000\nor, x= 14200 (approx)
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.
346484
theaccount balance after 12 years will be\n=2400*(1.019^24)
173316
I don't feel like working it out, but you just discount back the cash flows assuming they're constant, and then do some simple algebra.\n\nIt looks kind of like\n\n(785000 - 137) = (x / 1.07) + (x / 1.07^2) + ... (x / 1.07 ^10)\n\nSolve for x.
450211
The formula for continuously compounded interest is\nA = P e^(rt) where A = final amount, P = principal (initial amount), r = interest rate as a decimal, and t = time in years.  e is a mathematical constant.\n\nFor your equation, A = 4634 e^(0.08X4) = 4634e^0.32 = 6381.61\n\nSo the interest earned is 6381.61- 4634.00 = 1747.61\n\n\nTo find the effective rate, choose an arbitrary amount, say $100, that you can easily find 16% of.  Then find the actual interest.  The formula for quarterly compounding is\n\nA = P(1 + r/n)^(nt)  where all are as above and n = number of compoundings per year; here n = 4\n\nA = 100(1 + 0.16/4)^(4X1) = 116.98\n\nSo you actually earned 16.98 in interest which would be 16.98% of 100 so 16.98 is the effective yield.
6678
use $100\nfv=pv * (1+ I/compounding)^n*compounding \nn = years I = interest\nx = 100 * (1+.0425)^3*1 simple\nx = 100 * (1+.04/2)^3*2 compounded semiannually\nsimple = 113.30\nsemi annual = 112.62\nso simple is better over 3 years
663289
Do you mean the present value of annuity of 1 per year, for 48 years, at 8% per year compounded annually?\n\n\n(1-(1/1.08^48))/0.08 = 12.19
557333
You want to find how long the contract is for.  Using the compound interest formula,\nA(t) = A (1+r/n)^(nt) where A(t) is final value, A is starting value, r is interest rate, n is number of times interest is counted in a year, t is number of years. In this case we want to figure t.  Thus,\n\n(15000+1684.65) = 15000(1+.074/2)^(2)(t)\n16684.65 = 15000(1+.074/2)^(2)(t)\n16684.65/15000 = (1+.074/2)^(2)(t)\n1.11231 = (1+.074/2)^(2)(t)\n1.11231 = (1.037)^(2t)\nln (1.11231) = (2t) ln (1.037) \n2t = ln (1.11231) /ln (1.037) \n2t = 2.93\nt = 2.93/2 \nt = 1.47 \nSo the term of the contract is 1.47 years or almost one and half year.
190267
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
495219
Microsoft Excel can help with these kinds of calculations.  Though, an interest formula like this fails to take into account future additions to the principle of your retirement account.  Most people take some of each paycheck and put it into a retirement account rather than depositing a lump sum and forgetting about it.\n\nDon't forget to factor in inflation and taxes somehow!
109088
to be able to solve this, first you have to determine the amount of money in the fund after 30 years of annual deposit. to solve this you'll use the formula for annuity, which is,\n\nP = A [1 - (1+i)^-n] / i\n\nP = is the pricipal, in this case this would be the amount of the fund after 30 years.\n\nA = is the annual withdrawal, which is 50,000\n\ni = is the interest rate, which is 10%\n\nn = is the number of years, in this case it would be 20 years\n\nsubstitute the values of A, i, and n\n\nP = 50,000 [1 - (1 + .1)^-20] / .1\n\nP = 425678.19, this would be the amount of the fund after 30 year\n\nfrom this you can get the annual deposit in the account, you'll be using this formula,\n\nF = A [(1+i)^n - 1] / i\n\nF = is the future amount, in this case it would be the amount of the fund after 30 years, which is 425678.19\n\nA = is the annual deposit, which we are looking for\n\ni = is the interest rate, 10%\n\nn = is the number of years, this time it would be 30 years\n\nsubstituting,\n\n425678.19 = A [(1+.1)^30 - 1] / .1\n\nA = 2587.80
486751
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
37457
for question 1 is the return 8.242% per year? I would guess yes, so you would multiply 1.08242 to the 30th power times 10000. \n\nWhat you are doing here is to multiply 10,000 times 1.08242, (add the one to keep the 10000 plus interest, if you dont add the one you are only calculating the interest and have to add back in the 10000) to get how much at the end of year one, then multiply that result by 1.08242 to get what you have at end of year 2. Then keep doing that until at the end of year 30.\n\nThe second question is a bit more difficult. Take that spreadsheet and fill in the values at the top. make your begining value 10000 and the annual payment 0. Not sure what value to use for confidence (I am sure you know what to use here) and the other two were given return = 8%, deviation=10%. After 30 years you will have a lower and an upper limit. \n\nYou then take answer from #1 and find out how far into the range it is to find the percent liklihood. For example if the lower limit was 100 and the upper limit was 300 and your number calculate in #1 was 150, then you can see that 150 is greater than 25% of the possibilities and less than 75%. So you would do worse 25% of the time.\n\nThe actual calulation would be:\nU = Upper limit\nL = lower limit\nR = range = U - L\nC = compared value = answer from #1\n\npercent worse = (C-L)/R\n\nin the example percent worse = (150-100)/(300-100)
509745
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.....
667993
A.\n\nIn 19 years, it went up by a factor of 31.948.\n\n31.948^(1/19) = 1.20 = 20% increase every year.\nIn another 20 years, that's 31948 * (1.2^20) = 1224810