$400,000 for 30-years at a fixed APR of 3.87%. The loan payments are monthly and interest is compounded monthly.

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  1. what a deal!
    Oh - was there a question in there somewhere?

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  2. What is the effective annual rate on the loan? (I.e., what is the interest rate once we take into account compounding?)

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  3. We don't need the principal nor the time to find the effective annual rate

    All we are looking for it the annual rate i, which is equivalent to a rate of .0387/12 per month
    that is,

    (1+i)^1 = (1+.0387/12)^12
    1+i = 1.0393939

    i = .03939 or appr 3.939% (note, the decimals only appear to repeat at the beginning, they do not)

    check: take 100 for 5 years
    at 3.939..%
    amount = 100(1.03939...)^5 = 121.315
    at 3.87% compouned monthly,
    amount = 100(1 + .0387/12)^60 = 121.31
    well, how about that?

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