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Math Help - Amount of an Ordinary Annuity

  1. #1
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    Amount of an Ordinary Annuity

    Hi there.

    I've been trying a few questions for quite sometime and haven't been able to get to the correct answer.

    I would apperciate it if you could show me how to derive to the answer.

    Find the amount of each ordinary annuity.
    a. a payment of $1500 at the end of every 3 months at 8% per annum, compounded quarterly.

    b. a payment of $700 at the end of every month, into an account that pays 10% per annum, compounded monthly.

    c. a payment of $2800 at the end of every 6 months for 5 years with an interest rate of 9% per annum, compounded semi-annually.

    Thanks so much in advance
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  2. #2
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    Lexington, MA (USA)
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    Hello, asiankatt!

    There is a formula for these problems . . .

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

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

    I'll do the third one for you.
    For the others, we need to be told the number of years.



    Find the amount of each ordinary annuity.

    c. A payment of $2800 at the end of every 6 months for 5 years
    with an interest rate of 9% per annum, compounded semi-annually.

    We are given: . \begin{Bmatrix}D \,= \,2800 \\ i \, = \,\frac{9\%}{2} \,=\,0.045 \\ n = 2\!\cdot\!5\,=\,10\end{Bmatrix}<br />

    Therefore: . A \;=\;2800\,\frac{(1.045)^{10} - 1}{0.045} \:\approx\:\$34,406.99

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