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Math Help - Geometric sequence help...

  1. #1
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    Geometric sequence help...

    A person wants to borrow $100,000 to buy a house. He intends to pay back a fixed sum of $C at the end of each year, so that after 25 years he has completely paid off the debt. Assuming a steady interest rate of 4% per year, explain why:

    100,000 = C(\frac{1}{1.04} + \frac{1}{1.04^2} + \frac{1}{1.04^3} + ... + \frac{1}{1.04^{25}})

    I don't understand how is that even possible. If there's an interest rate of 4% per year, it should be a exponential growth, such that:

    Total payable sum = $ 100,000 * 1.04^{25} ~= 266584$ .. Dividing that by 25 gives $10,663 but that obviously isn't the answer.

    I have tried many other ways but I don't seem to get it
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  2. #2
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    Quote Originally Posted by struck View Post
    A person wants to borrow $100,000 to buy a house. He intends to pay back a fixed sum of $C at the end of each year, so that after 25 years he has completely paid off the debt. Assuming a steady interest rate of 4% per year, explain why:

    100,000 = C(\frac{1}{1.04} + \frac{1}{1.04^2} + \frac{1}{1.04^3} + ... + \frac{1}{1.04^{25}})

    I don't understand how is that even possible. If there's an interest rate of 4% per year, it should be a exponential growth, such that:

    Total payable sum = $ 100,000 * 1.04^{25} ~= 266584$ .. Dividing that by 25 gives $10,663 but that obviously isn't the answer.

    I have tried many other ways but I don't seem to get it
    Note that your first term is 1, your common ratio is 1/1.04 and there are 25 terms.

    From this you can use the sum of a geometric sequence:

    S_{25} = \frac{1(\frac{1}{1.04})^{25}}{1.04-1}
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  3. #3
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    hmm .. I am trying to figure out how do you get the common ratio as 1/1.04.
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