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Math Help - Series, Annuties

  1. #1
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    Question Series, Annuties

    if you deposit $1000 in your bank account yearly, and earn 5% interest per year, what is the formula for the nth term of this series?
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  2. #2
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    Hi

    Each year your money is multiplied by 1.05

    At the end of year n, you have got 1000 \cdot 1.05^n
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  3. #3
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    I tried this but it doesn't work, because after each year the 5% of interest has been added to the account plus the deposited $1000, and another 5% on interest is added t o this value. For example, after year 1 there is $1050 in the account to which another additional $1000 is added to make $2050, and the interest is added to get $2152.50.
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  4. #4
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    Hello, hsidhu!

    If you deposit $1000 in your bank account yearly, and earn 5% interest per year,
    what is the formula for the n^{th} term of this series?
    I assume you mean the balance at the end of n years.


    Annuity Formula: . A \;=\;D\,\frac{(1+i)^n-1}{i}

    . . where: . \begin{Bmatrix}<br />
A &=& \text{final balance} \\ D &=& \text{periodic deposit} \\ i &=& \text{periodic interest rate} \\ n &=& \text{number of periods} \end{Bmatrix}


    We have: . D = 1000,\;i = 0.05, and n periods.

    Therefore: . A \;=\;1000\cdot\frac{(1.05)^n-1}{0.05}

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