John invests $x at the semi-annual constant compounded rate of 2 percent and also does $40,000 at the quarterly constant compounded rate of 4 percent. If the interests are the same after 1 year, what is the value of x??  Choose the correct choice from the following answers:	A) 50000	B) 55000	C) 60000	D) 70000	E) 80804
A = P(1+r/n)^nt   A= total amount accrued   P = principal deposited   r = rate of interest in decimal form   n = number of times per year, interest compounded   t = time in number of years.   .   x(1+0.02/2)^2 - x = 40,000(1+0.04/4)^4 - 40,000 [ when the principal is subtracted from the total amount accrued , the resulting difference is the interest portion and question states interests are equal)   =&gt; x[(1.01)^2 - 1] = 40,000[(1.01)^4 - 1]   =&gt; x[(1.01)^2 - 1] = 40,000[(1.01)^2+1][(1.01)^2-1] --&gt; Using a^2-b^2 = a+b X a-b formula and cancel common expression on both sides   =&gt; x = 40,000(1.0201+1) =80804.   Hence answer is 80804.
<result>E</result>
John invests $x at the semi-annual constant compounded rate of 2 percent and also does $40,000 at the quarterly constant compounded rate of 4 percent. If the interests are the same after 1 year, what is the value of x??