Question

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
A(t)=P(1.00875)^4t

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.

Answer 1

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

Answer 2

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