P dollars is invested at annual interest rate r for 1year If the interest is compounded semiannually then the polynomial P(1+r/2)^2 represents the value of the investment after 1 year. rewrite the expressions without parentheses evaluate the polynomial if P=5670 and r=3.5%
5760(1+ .035/2)^2
5760(1 + 0.0175)^2
5760(1.0175)^2 = ?
5670(1+ .035/2)^2
5670(1 + 0.0175)^2
5670(1.0175)^2 = ?
To rewrite the expression without parentheses, we can expand the expression inside the parentheses.
The expanded expression is: P * (1 + r/2) * (1 + r/2).
When we multiply the terms within the parentheses, we get:
P * (1 + r/2 + r/2 + (r/2)*(r/2)).
Simplifying further, we have:
P * (1 + r + (r^2/4)).
Now, if we substitute P = 5670 and r = 3.5% (which can be written as r = 0.035), we can evaluate the polynomial.
Substituting the values, we get:
5670 * (1 + 0.035 + (0.035^2/4)).
Calculating the terms inside the parentheses, we have:
5670 * (1 + 0.035 + 0.001225).
Adding these values together, we get:
5670 * 1.036225.
Finally, evaluating the expression, we find that the value of the investment after 1 year is approximately:
5874.15 dollars.