# SOLUTION: Compound Semi Annually. P dollars is invested at annual interest rate r for 1 year. If the interest rate is compounded semiannually, then the polynomial P(1+r/2)squared presnts

Algebra ->  Algebra  -> Polynomials-and-rational-expressions -> SOLUTION: Compound Semi Annually. P dollars is invested at annual interest rate r for 1 year. If the interest rate is compounded semiannually, then the polynomial P(1+r/2)squared presnts      Log On

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 Question 92818: Compound Semi Annually. P dollars is invested at annual interest rate r for 1 year. If the interest rate is compounded semiannually, then the polynomial P(1+r/2)squared presnts the value of the investment after 1 year. Rewrite this expression without parenthesis. Evalate the polynomial if P=\$200 and r=10% I need help understanding this type of word problem.Answer by stanbon(57967)   (Show Source): You can put this solution on YOUR website!P dollars is invested at annual interest rate r for 1 year. If the interest rate is compounded semiannually, then the polynomial P(1+r/2)squared presnts the value of the investment after 1 year. Rewrite this expression without parenthesis. Evalate the polynomial if P=\$200 and r=10% --------- A(t) = P(1+(r/n))^(nt) Your Problem: Amount invested is P n = 2 meaning you compound the money twice in a year t is the number of years; in your case that is "1" r is the annual rate of interest -------------- A(1) = P(1+(0.10/2))^(2*1) A(1) = P(1.05)^2 A(1) = P(1.1025) ----------- If you expand the expression as you were directed you get: A(t) = P(1+(r/n))^2 = P[(1+(r/n))(1+(r/n))] = P[1 + 2(r/n) + (r/n)^2] ---------------- If P=\$200 and r=10% you get: A(1) = 200[1 + 2*0.05 + (0.05)^2] A(1) = \$220.50 ------------ Cheers, Stan H.