P dollars is invested at annual interest rate for 1 year. if the interest is compounded semiannually, then the polynomial p(1+r/2)^2 represents the value of the investment after 1 year. could you rewrite this expression without parentheses. Evaluate the polynomial if p = $200 and r = 10
(1+r/2)^2 = 1 + r + 1/4 *r^2
Put in the value of p, and r, and evaluate. I will be happy to critique your work or thinking.
Check my work.
To rewrite the expression without parentheses, we can expand the binomial using the formula (a+b)^2 = a^2 + 2ab + b^2.
Starting with the expression (1+r/2)^2, we can rewrite it as:
(1+r/2)(1+r/2)
Using the formula for multiplying binomials, we obtain:
1 + r/2 + r/2 + (r/2)^2
Simplifying the terms, we have:
1 + r + r/2 + r^2/4
Now, we can simplify the expression further:
1 + r + 1/2r + (1/4)r^2
Combining like terms, we get the final expression without parentheses:
1 + (3/2)r + (1/4)r^2
Now, let's evaluate the polynomial if p = $200 and r = 10:
Value = p(1+r/2)^2
Substituting in the given values, we have:
Value = $200(1+10/2)^2
Value = $200(1+5)^2
Value = $200(6)^2
Value = $200(36)
Value = $7200
Therefore, if p = $200 and r = 10, the value of the investment after 1 year is $7200.