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Thread: a=(1+r/n)^nt

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    a=(1+r/n)^nt

    Compound Interest Formula. My professor said this one equation ruined the lives of many. What does he mean by this?


    Also, what is the point of learning A=pert? He said it is continuous interest, yet it is never used in real life.
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    Re: a=(1+r/n)^nt

    I suggest you ask him.

    $A=pe^{rt}$ is the limit case for large $n$, so it will serve as a good approximation to whatever the actual situation is. The equation is particularly easy to deal with mathematically while the discrete case is much less so.
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    Re: a=(1+r/n)^nt

    Quote Originally Posted by math951 View Post
    Compound Interest Formula. My professor said this one equation ruined the lives of many. What does he mean by this?


    Also, what is the point of learning A=pert? He said it is continuous interest, yet it is never used in real life.
    re the first question there's a reason that usury was outlawed by the ancients. Consider a typical mortgage on a house. Let's say the house is \$250,000.

    We purchase this house with a 30 year mortgage at say 3% interest. These are realistic numbers for today. Let's further say that interest is compounded monthly.

    The actual price of the house then is $C = \left(1 + \dfrac{.03}{12}\right)^{12\times 30} \times \$250000 = \$614,210.55$

    With what looks to be a very typical mortgage you are paying about 2.5 times the original cost of the house.


    Interest that is compounded continuously would be the usual sort of loan with n tending towards 0. It's never used because you would have to make $\dfrac 1 n$ payments and this is clearly impossible. It is essentially the case you making tiny payments constantly and you would like to be able to do something with your life other than hand a bank teller pennies.
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    Re: a=(1+r/n)^nt

    Quote Originally Posted by romsek View Post
    re the first question there's a reason that usury was outlawed by the ancients. Consider a typical mortgage on a house. Let's say the house is \$250,000.

    We purchase this house with a 30 year mortgage at say 3% interest. These are realistic numbers for today. Let's further say that interest is compounded monthly.

    The actual price of the house then is $C = \left(1 + \dfrac{.03}{12}\right)^{12\times 30} \times \$250000 = \$614,210.55$

    With what looks to be a very typical mortgage you are paying about 2.5 times the original cost of the house.
    You have forgotten that the borrower makes payments back to the bank/institution. That means that it is actually an annuity / reducing balance loan.

    So the actual price of the house won't be quite that much, but will still be worth a lot more than the original mortgage.
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    Re: a=(1+r/n)^nt

    Quote Originally Posted by Prove It View Post
    You have forgotten that the borrower makes payments back to the bank/institution. That means that it is actually an annuity / reducing balance loan.

    So the actual price of the house won't be quite that much, but will still be worth a lot more than the original mortgage.
    Same numbers end up with

    $C=\$379444.00$ so about 1.5 times the cost of the house. Given this it's probably more likely your teacher is referring to loan sharks rather than mortgages.
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