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College Algebra

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bank a is lending money at 5.7% interest compounded annually. The rate at bank b is 5.6% compounded monthly, and the rate at bank C is 5.65% compounded quarterly. Which bank will you pay the least interest?

  • College Algebra -

    Bank A: Pt = Po(1+r)^n.
    r = 5.7%/100% = 0.057 = APR expressed as a decimal.
    n 1comp/yr * 1yr = 1 compounding period.
    Pt = 1(1.057)^1 = 1.057.

    Bank B: Pt = Po(1+r)^n.
    r = (5.6%/12) / 100% = 0.00467 = Monthly % rate expressed as a decimal.
    n = 1comp/mo * 12mo = 12 Compounding
    periods.
    Pt = 1(1.00467)^12 = 1.058.

    Bank C: Pt = Po(1+r)^n.
    r = (5.65%/4) / 100% = 0.014125 = Quarterly % rate expressed as a decimal.
    n = 4comp/yr * 1yr = 4 Compounding periods.
    Pt = 1(1.014125)^4 = 1.058.

    The amt. charged by each bank is approximately the same.

    Note: All calculations were done with the assumption that $1.00 was borrowed from each bank for a period of one year.

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