SOLUTION: Hi, can someone help with the following? 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)s

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi, can someone help with the following? 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)s      Log On


   

Question 81518: Hi, can someone help with the following?
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)squared represents the value of the investment after 1 year. Rewrite this expression without parentheses. Evaluate the polynomial if P=$200 and r=10%
Answer by dolly(163) About Me  (Show Source):
You can put this solution on YOUR website!
Given the value of investment after 1 year is :
V = P(1 + r/2 )^2
==> V = P (1 + r + r^2/4) [using (a+b)^2 = a^2 + 2ab + b^2]
==> V = P + Pr + Pr^2/4
This is the required polynomial.
When P = 200 and r = 0.1 then,
V = 200 + 200(0.1) + 200(0.1)^2/4
= 200 + 20 + 0.5
= 220.5
Thus the value of the investment of $200 after 1 year at 10% is $ 220.5