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Exponential Word Problem

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An investment pays 3.5 percent interest, compounded quarterly.
a) write an equation to express the amount A, of the investment as a function of time, t, in years.

The answer is

Ok, but my question is this:
Why isn't the equation
A(t)=P(1.035)^4t, if the interest percent is 3.5% wouldnt it make sense that it's 1.035 in the equation and not 1.00875. Could someone clarify for me if I am right or wrong, and why.

  • Exponential Word Problem -

    The 3.5% is expressed PER YEAR by convention, thus 3.5 / 4 = .875% per quarter year compounding period.

  • Exponential Word Problem -

    Note that 1.00875^4 = 1.0355
    That 3.5% is really 3.55% in effect because it is compounded quarterly.

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