A bank credit card charges interest at the rate of 22% per year, compounded monthly. If a senior in college ch?

A bank credit card charges interest at the rate of 22% per year, compounded monthly. If a senior in college charges $2,100 to pay for college expenses, and intends to pay it in one year, what will she have to pay? (Round your answer to the nearest cent.)

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  • 9 years ago
    Favorite Answer

    So you borrow $2100 at the beginning of year and intend to pay it all back along with interest at the end of year.

    nominal interest rate = i = 22%

    n = number of periods = 12

    The effective interest rate = r = (1+i/n)^n - 1 = (1 + 0.22/12)^12 - 1 = 0.2436 or 24.36%

    payment = $2100 * (1+r) = $2611.56

  • L = loan amount = 2100

    i = 22% = 0.22

    P = payment

    L = P/(1 + i/12) + P / (1 + i/12)^2 + ... + P / (1 + i/12)^12

    L = P * sum((1 + i/12)^(-t) , t = 1 , t = 12)

    Let 1/(1 + i/12) = r

    L = P * sum(r^t , t = 1 , t = 12)

    S = r + r^2 + r^3 + ... + r^12

    S * r = r^2 + r^3 + ... + r^12 + r^13

    Sr - S = r^13 - r

    S * (r - 1) = r * (r^12 - 1)

    S * (1 - r) = r * (1 - r^12)

    S = r * (1 - r^12) / (1 - r)

    L = P * r * (1 - r^12) / (1 - r)

    L * (1 - r) / (r * (1 - r^12)) = P

    r = 1 / (1 + i/12)

    r = 1 / ((12 + i) / 12)

    r = 12 / (12 + i)

    r = 12 / (12 + 0.22)

    r = 12 / (12.22)

    L * (1 - (12 / 12.22)) / ((12 / 12.22) * (1 - (12/12.22)^12)) = P

    P = 2100 * ((12.22 - 12) / 12.22) / ((12 / 12.22) * ((12.22^12 - 12^12) / 12.22^12))

    P = 2100 * (0.22) * 12.22^12 / (12 * (12.22^12 - 12^12))

    P = 2100 * 0.09359437964208574225766219148281

    P = 196.5481972483800587410906021139

    $196.55 a month

  • Bevvy
    Lv 6
    3 years ago

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    RE :A bank credit card charges interest at the rate of 22% per year, compounded monthly. If a senior in college ch?

    A bank credit card charges interest at the rate of 22% per year, compounded monthly. If a senior in college charges $2,100 to pay for college expenses, and intends to pay it in one year, what will she have to pay? (Round your answer to the nearest cent.)

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    Source(s): For Credit and finance solutions I recommend this website where you can find all the solutions. http://LOANSANDFINANCES.INFO/index.html?src=5YAPZP...
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