Math CentralQuandaries & Queries


Question from Vincent, a student:

Compounded semiannually. P dollars is invested at annual interest rate r for 1 year. If the interest is compounded semiannually, then the polynomial P(1 + r/2)2 represents the value of the interest after 1 year. Rewrite this expression without parentheses. Evaluate the polynomial if P=$200 and r = 10%.

Hi Vincent,

The polynomial P(1 + r/2)2 is equivalent to P(1 + r/2)(1+r/2) . Sometimes students have a hard time distributing factors that contain fractions. For this situation I suggest substituting the fractional term with a variable then substitute back:

Let c = r/2

P(1+c)(1+c) = P(1+c+c+c2)= P(1+2c+c2)=P+2Pc+Pc2=P+2P(r/2)+P(r/2)2 = P+Pr+Pr2/4

Now you can substitute P=200 and r=0.10 into your bracket-free polynomial.

Hope this helps,


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