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Math Help - solve for interest rate

  1. #1
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    solve for interest rate

    Hello, I am looking for the formula to solve for interest rate. I know to following:

    Initial Loan Amount: $100,000
    Term (years or months): 30/360
    Monthly payment: $536.82
    twelve pay periods per year

    correct answer 5.50%

    Thank you
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  2. #2
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    What formula(s) did they give you for this homework exercise? Perhaps we can work from there.
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  3. #3
    Senior Member pacman's Avatar
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    Problem: Initial Loan Amount: $100,000
    Term (years or months): 30/360
    Monthly payment: $536.82
    twelve pay periods per year
    correct answer 5.50%

    ----------------------------------------------------------------
    Solution:

    Let:
    r = the yearly nominal interest rate. t = the number of years. m = the number of periods per year. i = the interest rate per period. n = the number of periods. Note:
    n = tm Also let:
    P
    = the principal (or present value). R = the periodic payment in an annuity (the amortized payment).
    Also: .


    P = $100,000.00,
    t = 30 year,
    R = $536.82
    m = 12 periods in 1 year,
    i = r/m = r/12,
    n = tm = 30(12) = 360

    --------------------------------------------------------

    using this Formula: .

    100000 = (536.82)(1 - (1/(1 + r/12)^360))/(r/12),

    100000/536.82 = (12/r)[1 - (1 + (r/12))^-360]

    (100000/536.82)(r/12) = 1 - (1 + (r/12))^-360

    (1 + (r/12))^-360 = 1 - (100000/536.82)(r/12) = 1 - 15.524r

    1 = (1 - 15.524r)(1 + (r/12))^360,

    wow! what a big number, i will use substititution.

    The only thing that equals the left hand side is when r = 0.04999999 is used at the right hand side of the equation.

    so, r = 0.049999 = 0.05 = 5% = nominal rate of interest.

    effective rate of interest = (1 + 0.05/12)^12 - 1 = 1.05116 - 1 = 0.05116 = 5.116%

    My answer differs greatly. . . . i can not find where is my mistake.
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