Math Lovers here is one for you?

Question

This is 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 investment after 1 year. Rewrite the expression without parentheses. Evaluate the ploynomial if P=$200 and r = 10%

Answer 1

200(1+.10/2)^2 or 200(1.05)^2 or 200 * ((1.05)(1.05)) or 200 * 1.1025 or $220.50

The elementary way to change this equation is

P ((1+r/2)(1+r/2))

Using the FOIL method

P((1 + r/2+r/2+(r/2)*(r/2))

Switching the equation up a little to correct for order of operations (r/2=1/2 * r or r *1/2)

P((1 + r/2+r/2+((r * 1/2)*(r*1/2))) or P((1 + r/2 + r/2+((r^2)/4)

Combining like fractions

P*(1 + 2r/2 + r^2/4)

Reducing fractions

P*(1 + r + r^2/4)

Distributing the P

P * 1 + P * r + P * r^2/4


Using numbers

200*1+200*.10+200*.10^2/4

or

200 + 20 + 200*.01/4

or

200 + 20 + 2/4

or

200 + 20 + .5

or

$220.50


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