A family wants to have a $2000,000 college fund for their children at the end of 20 years.  What contributions must be made at the end of each quarter if their investment pays 7.6%, compounded quarterly?
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)
503940
5% of $1500= $75\n20% of $1500= $300
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.
473914
She invests some portion of the 4500, call it x, in the 5% vehicle, and the remainder (4500-x) in the 9% vehicle.  She wants to earn 250 per year ... it depends on how often the interest is compounded, but since annual interest is the easiest I will assume that's what you'd use for your HW problem (unless you are in an advanced econ. class or something!).\n\nSo you have 250 = 0.05x + .09(4500-x), which you can easily solve for x from.
532844
If you compound the interest (add the interest earned back into the principle) once a year, you get 6%. If you stop every three months, add the interest into the principle and start again, you'll have more money at the end of the year by accruing interest on the interest earned-to-date. \n\nSay 6% per year, works out to 1.5% for one quarter. Instead of investing $100 for a year, you invested $100 for one quarter and made $1.50. Then next quarter, you invest $101.50, by the third quarter you have $104.57, and at the end of the year you have $106.14. Because you invested the interest earned too. In finance, money*time = more money, so it's better to get your earnings ASAP instead of at the end of the year (e.g. daily compounding).
197210
set up the diffeq:\n\ndM/dt=1.05*M+alpha //money accrued at rate of 5.5% per year plus some amount alpha that is placed into the accout per year\ndm/dt=1.05*m -45000 //rate spent per year after retirement (assuming interest continues to accrue)..\nM(0)=162000; //intial ammount in retirement fund\nM(15)=m(0) //retirement fund begins expenditure with intial value of total saved + interest, or M(15)...\n\n// Note: 12 is measured from date of retirement...\nm(12)=0; //money only lasts 12 years, assume total amount expended...\nsolve dm/dt and plug in m(12)=0 to figure out what the total saved, m(0), must be present at the beginning of retirement in order to completely expend the money in the 12 yr period\n\nfinally, solve for M(t) and use the known values at M(0) and M(15) to compute the value of alpha.
187100
This depends solely on the terms of your fellowship. I invested student loans while doing my undergraduate, made a7.5% return on them while paying for school on a 0% interest credit card each year. I paid off the loans at no interest (because I only took out the $8500 max each year from the feds) and made a pile in interest.
144226
It depends if it's simple interest or compound (sometimes called effective interest).\n\nI'm also assuming that the 6.5% is per year.\n\nThe accumulation factor formula (ie what we multiply our initial amount by) for simple interest is:\n\n(1 + ni)\n\nSo if we double our initial amount then this factor must be 2.\n\n1 + 0.065n = 2\n\nThis gives\n\n15.38 years (I am assuming that you receive this interest daily - and not at the end of each year or anything like that)\n\nThe accumulation factor formula (ie what we multiply our initial amount by) for compound interest is:\n\n(1 + i)^n\n\nSo if we double our initial amount then this factor must be 2.\n\n1.065^n = 2\n\nTo solve this we need to take logs:\n\nln (1.065^n) = ln 2\n\nWe then use the rule that ln (a^b) = b ln a\n\nn ln 1.065 = ln 2\n\nSo:\n\nn = ln 2 / ln 1.065 = 11.007 years\n\n(Again I'm assuming that you receive this interest daily - and not at the end of each year or anything like that)\n\n(PS you can use other logs as well for this - it doesn't make a difference here)
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
594920
A simple trust might not be the best way to go.\n\nTrusts are taxed at higher rates than people with fewer exemptions (gross oversimplification but it's true) -- I'm an IRS phone rep and know from whence I speak.\n\nTrusts require professional trustees and advisors and those ain't cheep!\n\n And if these "kids" are (old enough to be your grand)kids, you could get gouged with generation-skipping tax!\n\nHave you talked with your financial advisor? Many states offer prepaid tuition bonds and instruments that accumulate value tax free.\n\nAlso if kids are young you might want to set up bank accounts for each of them individually. Teach them the value of saving while you help them reach their goals.\n\nAnd one last -- most important thought -- If you invest in government instruments that accumulate tax free interest, you can use the proceeds to pay your four kids' tuition without (Federal) tax -- provided you pay the college directly.\n\nGood luck, Cincypix
217769
If your talking a single $20.00 bill, your wife or mothers birthday is a great investment. If you have $20.00 a week to spare, stick with the obvious. My choice would be a Mutual Fund. You would be suprised how quickly it will add up.
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.
495690
assume $Y grows at 10% every year. after 1year\ninterest=Y*(1.1^1)-Y\n\nSo after X years\ncompound interest= Y*(1.1^X)-Y\n\nan example: $1000 grows at 10% every year for 20 year will have compound interest of\n1000(1.1^20)-1000=$5727.5   ( as suppose to $2000 which is what you will have if you earn 10% every year but not compound)\n\nAnother one: $1000 grows at 15% every year for 20 year will have compound interest of\n1000(1.15^20)-1000=$15366   ( as suppose to $3000 which is what you will have if you earn 15% every year but not compound)\n\nenjoy
374356
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.
195698
Please check:\nhttp://moneycentral.msn.com/content/CollegeandFamily/Savingforcollege/P59866.asp\n\nGood Luck\nNBS
309458
A=P(1+r/n)^(n*t)\nA = 20,000(1+.08/1)^(1*3)\nA = 20,000(1.08)^3\nA = 25,194.24\n\nThe more frequently you compound, the more money you will make.\n\nA = Pe^(rt)\nA = 20,000e^(.08*3)\nA = 20,000e^.24\nA = 20,000(1.271249150)\nA = 25,424.98
470752
well, you didn't mention the compounding factor, so....\n\nsimple interest\nA sub t is the value (amount) after "t" time\nP is the initial amount invested\nr is the interest rate\nt is time ( in years)\n\n    A sub t  = P ( 1 + r) ^ t\n\nfor compound interest rate\nn is the number of times that the interest is compounded per year\n\n    A sub t = P ( 1 + r/n) ^ (n*t)\n\n\nnow, you have another problem...\nsome CDs only pay interest yearly....\nsome quarterly, some monthly...\nsince your interest rate is different from your APR, \nI'll assume a monthly compounding\n\n     Amt = $2000 ( 1 + (.0489/12)) ^ (12* (11/12))\n\nnote: the  time is 11/12 because interest is figured on a yearly basis and 11 months is 11/12 of a year\n\n  if my calculator does not deceive me\nyou should get   $2091.50