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Math Help - Compound Interest Savings Account

  1. #1
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    Post Compound Interest Savings Account

    Hi All

    I am new to this forum, so I hope you would not mind the links in this message as I needed to list them to explain my query.

    I design, develop and host online graphing, scientific, statistical and financial calculators at http://www.thinkanddone.com

    That said, I was working on design of a Savings Account calculator that I need help with formulas. Doing a search on web, I found Professor Grant Lythe's (Uni of Leeds) notes

    Example

    Let us consider the example of a savings account that pays 6% interest compounded monthly. Suppose a saver deposits $1000 on the first day of every month. What is the account
    balance at the end of 2 years

    I found the following formula to compute the balance at end of n period

    r is the interest rate
    p = 1 + (1/12)(r/100)
    A = 1000 p ( (p^n)-1 )/(p-1)
    A = 25559.12

    I compared my results to an online calculator at Savings Calculator - Financial Calculators from Dinkytown.net

    So far so good.

    But like the calculator, I am trying to compute balance by changing either the compounding period to daily, quarterly and yearly
    or the deposit interval to weeky, biweekly, per quarter and per year

    How can I change the formula I mentioned at top for these option

    I will post a different question about continuous compounding of interest as the calculators I used on Aussie bank sites show different
    answer to the result above so I assume they use continuous compounding of interest . ( Finance calculators - financial comparisons and information from Infochoice )
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  2. #2
    Member jonah's Avatar
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    Quote Originally Posted by dexteronline View Post
    Let us consider the example of a savings account that pays 6% interest compounded monthly. Suppose a saver deposits $1000 on the first day of every month. What is the account
    balance at the end of 2 years

    I found the following formula to compute the balance at end of n period

    r is the interest rate
    p = 1 + (1/12)(r/100)
    A = 1000 p ( (p^n)-1 )/(p-1)
    A = 25559.12

    But like the calculator, I am trying to compute balance by changing either the compounding period to daily, quarterly and yearly
    or the deposit interval to weekly, biweekly, per quarter and per year

    How can I change the formula I mentioned at top for these option
    <br />
\ddot S = R \cdot \frac{{\left( {1 + {\textstyle{j \over m}}} \right)^{tm}  - 1}}{{{\textstyle{j \over m}}}} \cdot \left( {1 + {\textstyle{j \over m}}} \right) = 1,000\frac{{\left( {1 + {\textstyle{{.06} \over {12}}}} \right)^{2 \times 12}  - 1}}{{{\textstyle{{.06} \over {12}}}}} \cdot \left( {1 + {\textstyle{{.06} \over {12}}}} \right)<br />

    To compute balance by changing either the compounding period to daily, quarterly and yearly, just change m to 365, 4, and 1. Make sure the deposit interval is the same as the interest compounding/conversion period.
    If not, contemplate this.
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  3. #3
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    I had come to the right forum: Thanks Jonah

    Jonah

    The continuous compounding formula is what the banks in Australia are using for their Savings Calculator at Bank of Queensland, Savings calculator

    And your provided formula produces the result, how would I adjust this continuous compounding formula if there is an initial invest along with periodic deposits. Say an initial deposit of $2000 and monthly payments of $1000 for 2 years at 6%

    Jonah I have been developing these online tools for the last two years, I had converted on of them to Desktop Version which allows graphing f(x) in coordinate plane, Here is where you can download it http://www.thinkanddone.com/ge/GraphEasyRect.jar

    You would need Java Runtime Environment to be installed for the program to run MS Windows, Linux or Mac OS .

    You can download the JRE from SunSoft site at Download Java 2 Platform, Standard Edition, v 1.4.2 (J2SE)

    This forum has opened new venues for me. As I am always looking for new ideas to develop calculator, now I know where to get help when looking for help with formulas

    Asad S. Yousaf
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  4. #4
    Member jonah's Avatar
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    Quote Originally Posted by dexteronline View Post
    And your provided formula produces the result, how would I adjust this continuous compounding formula if there is an initial invest along with periodic deposits. Say an initial deposit of $2000 and monthly payments of $1000 for 2 years at 6%
    If the monthly payments of $1000 were made at the beginning of every month and your nominal rate of 6% is compounded continuously, then

    <br />
2,000e^{0.06 \times 2}  + 1,000\frac{{e^{0.06 \times 2}  - 1}}{{e^{{\textstyle{{0.06} \over {12}}}}  - 1}} \cdot e^{{\textstyle{{0.06} \over {12}}}} <br />

    If the monthly payments of $1000 were made at the end of every month, then

    <br />
2,000e^{0.06 \times 2}  + 1,000\frac{{e^{0.06 \times 2}  - 1}}{{e^{{\textstyle{{0.06} \over {12}}}}  - 1}}<br />

    You might want to check this and this out for a more comprehensive layout. You can read them online (disadvantage: a few pages are missing) or you can order them online.

    The fourth edition of Dr. Broverman's book with its corresponding solutions manual is now available. Just follow the threads.
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  5. #5
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    Thanks Jonah

    Jonah

    Thanks for taking time to answer my questions. I think these books will be of great help

    Asad S Yousaf
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