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Compound interest, what is it ?

  1. Jun 8, 2009 #1
    I know interest is compute by formula

    interest=(All money person get) - expense

    but I hear there say compound interest, what is it ?
    after all how many interest is there ?

    Thank you
  2. jcsd
  3. Jun 8, 2009 #2
    Re: interest

    Only the one you have to understand life problems.

    Hi there,

    I am not an economist, but your equation does not seem right to me. The money you gain less your expenses is not considered to be an interest, but the left over from your wage.

    Now, if you decide to put this left over in a bank (instead of spending on beer), the bank will offer you some money for it, called the interest. To encourage to put some more money in an account, a bank will say that they give you 3% of interest annually on the money you put there.

    The idea behind compound interest lies in the fact that you leave your money at the bank for a longer period of time. To make it simple, let's take an example: you put 100$ at 3% annual interest rate. At the end of the first year, your bank account will show 103$ (100$ base + 3$ interest). The second year, the 3% interest rate is not on 100$, but on 103$. Therefore, at the end of the second year, your bank account would show 106.09$. As you can see, there is 0.09$ more than the first year. If you leave you money in the bank for a third year, your bank account would show 109.2727$. And so on.

    As you can see, your 3% interest is compound by the interest money left in the account.

    Hope this is more clear now.

  4. Jun 8, 2009 #3
    Re: interest

    That's not the formula for interest, the formula for profit is:
    profit = (All money person get) - expense
    The formula for interest is
    interest = principle x interest rate
    The formula for compound interest in the first period is the same. However in the second period simple interest is
    interest = principle x interest rate
    but compound interest is
    interest = (principle x (1 + interest rate)) x interest rate
    For instance, if the principle is $100, and the interest rate is 5%, the for the first two years, the simple interest is:
    1st year $5
    2nd year $5
    while compound interest is
    1st year $5
    2nd year $5.25
    In the second case, you are getting interest on your interest. That's what compounding means.
  5. Jun 8, 2009 #4


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    Staff Emeritus
    Science Advisor

    Re: interest

    Interest is basically the cost of money, or the cost of borrowing money.

    Compound interest is effectively interest on the unpaid interest in addition to the principal or money borrowed. It's the same as interest on savings.

    In savings, one places money in an account and the bank or financial institution uses that money for investment. If one puts in $1000 and receives 5% (interest rate) per period (where period = month, quarter, or whatever), the in one period on earns $50. Now if one leaves the money in the account, at the end of the next period, one receives another $50 on the initial investment of $1000, and $2.50 on the interest earned during the previous period.

    Over n periods one earns $1000*(1.05)n of money and the total interest earned is $1000*[(1.05)n-1].
  6. Jun 8, 2009 #5
    Re: interest

    I am clearified. Thank you :smile:

    But is there a pure profits and other kind of profits too ?
  7. Jun 8, 2009 #6


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    Staff Emeritus
    Science Advisor

    Re: interest

    Sure profit is the difference between revenues (or gross income) and expenses (including taxes).

    Let's say one invests $1000 in company and then sells the investment (usually stock) for $10000. One has made a gross profit of $9000. But let's say one pays 20% tax on the $9000 profit. Then one's net profit is $7200. If one pays other fees, e.g. fee for the investment transactions, then one's profit will be less.
  8. Jun 8, 2009 #7
    Re: interest

    As Astronuc pointed out, there is
    gross profit = income - expense
    net profit = income - expense - tax
    Which of these is pure probably depends on your politics. For Socialists, probably neither is pure.
  9. Jun 8, 2009 #8


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    Staff: Mentor

    Re: interest

    I think an easier way to explain compound interest is that "compounding" is just the frequency with which the interest is calculated.

    If you start with $100 and have 12% interest and calculate (compound) it annually, then at the end of 1 year you'll have $112, after two you'll have $125.44, three you'll have $140.49.

    But if you compound it monthly, then after 1 month you'll have $101 (1/12th of 12%), two months you'll have $102.01, three months $103.03.....and 12 months $112.68, two years $126.97, and three years, $143.08.

    Compounding maximizes the interest earned by ensuring you are always earning intrest on top of interest: most bank accounts and loans are compounded continuously.

    Some fixed-income investments such as CDs are not compounded at all (unless you automatically roll them over after they mature...).
  10. Jun 8, 2009 #9
    Re: interest

    Both simple and compound interest have a frequency of calculation. For instance $100 at 12% annual simple interest would generate $12 a year for the duration of the transaction. The same would be true of 1% monthly simple interest.
  11. Jun 8, 2009 #10


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    Staff: Mentor

    Re: interest

    Huh, I stand corrected. Here's the wiki on it... http://en.wikipedia.org/wiki/Interest#Simple_interest

    I guess, though, since you don't pay interest on interest in a simple interest loan, you can't ever do more frequent calculating than once per payment period.
  12. Jun 8, 2009 #11
    Re: interest

    As I understand you are want to know how many different kind of interests are there.

    Looking at all the earlier posts, I couldn't find anyone
    1) making a distinction between real and nominal
    2) taking into account inflation

    Real profits (or pure if you meant that by real) are not equal to accounting profits where you account for deprecations etc.

    You need to go beyond mathematical definition if you are doing some accounting/financial stuff else I don't think you need to know depreciation/inflation/nominal (might need to know nominal vs real) so you may ignore this post.
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