Financial Polynomials

Solve problem: P dollars is invested at annual interest rate r for 1 year. If the interest is compounded semi-annually, then the polynomial P(1+r/2)^2 represents the value of the investment after 1 year. Rewrite this expression without parentheses. "P" is represented as the value of invested money "r" is represented as the interest rate offered for this investment "A" represents the amount of money that is due for this investment P(1+r/2)2 represents the value of the investment after 1 year or simply the "A" We are required to rewrite the equation P(1+r/2)2 thus we get: A= P(1+r/2)2 = P(1+r/2)*( 1+r/2) * We show that the parenthesized equation is squared to remove the square = P(1+r2+r) *This is the result when we multiply 1+ r with 1+ r 4 2 2 =P+Pr+Pr2 *This is now the resulting equation as we have multiplied the "P" to both 4 elements inside the parenthesis. Now, for the evaluation: Evaluate the polynomial resulting from step 1 using:P = $200 and r = 10%, and also withP = $5670 and r = 3.5% Evaluate the polynomial if P=$200 and r=10%.A= P+Pr+Pr2 4 *First, we substitute the representations with their given values A= $200+$200*0.10+$200*0.102 4 A=$200+$200*0.10+$200*0.0100 *Notice that we have now squared the value of 0.10 4 A=$200+$20+$0.5 *We have now simplified the second and the third terms. -32385-3810000A= $220.5 *We now have the solved value for A. P = $5670 and r = 3.5% A= P+Pr+Pr2 4 A=$5670+$5670*0.035+$5670*0.0352 4 A=$5670+$5670*0.035+$5670*0.001225 *Notice that we have now squared the value of 0.035 4 A=$5670+$198.45+$1.7364375 *We have now simplified the second and third terms. -7429521018500 A=$5870.1864375 ...