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 investment after 1 year. Rewrite this expression
without parentheses. Evaluate the polynomial if
P = $200 and r = 10%.
Value = P + Pr + Pr^2/4
Plug in the numbers.
$20,000+1+6.2^-6
To rewrite the expression without parentheses, you need to expand the equation using the distributive property.
The equation is: P(1 + r/2)^2
Expanding it, we have: P(1^2 + 2*(1)*(r/2) + (r/2)^2)
Simplifying it further, we get: P(1 + r + r^2/4)
Now, you can substitute the given values P = $200 and r = 10% = 0.10 into the equation.
So, the final expression becomes: 200(1 + 0.10 + (0.10)^2/4)
Now, evaluate the expression:
= 200(1 + 0.10 + 0.01/4)
= 200(1 + 0.10 + 0.0025)
= 200(1.1025)
= $220.50
Therefore, the value of the investment after 1 year, compounded semiannually with P = $200 and r = 10% is $220.50.