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Thread: Compound Amount and Interest: $10K invested for 5 yrs at 12%

  1. #1

    Compound Amount and Interest: $10K invested for 5 yrs at 12%

    One of the problems on my homework is:

    Find the compound amount and compound interest is $10,000 is invested for 5 years at 12% interest compounded monthly.

    I did:

    $10,000*(1+.01)^60 and got $18,166.97.

    -I know this is my compound Interest but I'm confused because the question says find the compound amount AND interest.

    Is that all I do or do I have to keep going and do somthing else?

  2. #2
    Full Member
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    Re: Compound Amount and Interest?

    [quote="notamathguy11"]One of the problems on my homework is:

    Find the compound amount and compound interest is $10,000 is invested for 5 years at 12% interest compounded monthly.

    I did:

    $10,000*(1+.01)^60 and got $18,166.97.

    -I know this is my compound Interest but I'm confused because the question says find the compound amount AND interest.

    With compound interest, the interest due and paid at the end of the interest compounding period is added to the initial starting principal to form a new principal, and this new principal becomes the amount on which the interest for the next interest period is based. The original principal is said to be compounded, and the difference between the the final total, the compound amount, accumulated at the end of the specified interest periods, and the original amount, is called the compound interest.

    In its most basic use, if P is an amount deposited into an account paying a periodic interest, then Sn is the final compounded amount accumulated where

    ..........................Sn = P(1+i)^n

    where i is the periodic interest rate in decimal form = %Int./(100m), n is the number of interest bearing periods, and m is the number of interest paying periods per year.

    For example, the compound amount and the compound interest on $5000.00 resulting from the accumulation of interest at 6% annual interest compounded monthly for 10 years is as follows:

    Since m = 12, i = .06/12 = .005. Since we are dealing with a total of 10 years with 12 interest periods per year, n = 10 x 12 = 120. From this we get

    .........................Sn = $5000(1+.005)^120 = $5000(1.8194) = $9097.

    Consequently, the compound interest realized is $9097 - $5000 = $4097. Of course the compound interest rate can be calculated directly from the simple expression

    .........................I = P[(1+i)^n - 1].

    The interest associated with annuities, loans, mortgages, savings accounts, IRA's, etc. are all based on the compound interest principle. Some additional applications of the use of compound interest are offered below.
    TchrWill

    No matter how insignificant it might appear, learn something new every day.

  3. #3
    Senior Member
    Join Date
    Aug 2007
    Posts
    1,303

    Re: Compound Amount and Interest?

    Quote Originally Posted by notamathguy11
    One of the problems on my homework is:

    Find the compound amount and compound interest is $10,000 is invested for 5 years at 12% interest compounded monthly.

    I did:

    $10,000*(1+.01)^60 and got $18,166.97.

    -I know this is my compound Interest but I'm confused because the question says find the compound amount AND interest.

    Is that all I do or do I have to keep going and do somthing else?
    If you put money in the bank and leave it there for so many years, you will have more money at the end of that time than what you had at the start. What you have at the end is the "amount". The difference between the amount and what you invested is the interest. It goes like this...
    Amount invested + amount of interest = Amount you have at the end of the time period.
    Remember to distinguish between the RATE of interest and the AMOUNT of interest. Both of these are frequently referred to as "the interest".

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