SOLUTION: Compounded semi-annually. 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

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Compounded semi-annually. 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       Log On


   

Question 189665: Compounded semi-annually. 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 the investment after 1 year. Rewrite this expression without parenthesis. Evaluate the polynomial if P=$200 and r = 10%.
this is the answer I got
a. P + 2²P+ Pr²
b. 200(1+ 10/100.2)^2
200(1+0.05)^2 = 200 multiply 0.0025 =$50.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a)


P%281+%2B+r%2F2%29%5E2 Start with the given expression.


P%281%2B2%28r%2F2%29%2Br%5E2%2F4%29 FOIL


P%281%2Br%2Br%5E2%2F4%29 Multiply


P%2BPr%2BP%28r%5E2%2F4%29%29 Distribute


P%28r%5E2%2F4%29%2BPr%2BP Rearrange the terms.


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b)


There are two ways to do this:

Method #1:


P%281+%2B+r%2F2%29%5E2 Start with the original expression


200%281+%2B+0.1%2F2%29%5E2 Plug in P=200 and r=0.1


200%281+%2B+0.05%29%5E2 Divide


200%281.05%29%5E2 Combine like terms.


200%281.1025%29 Square 1.05 to get 1.1025


220.5 Multiply


So after a year, we have $220.50 in the account

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Method #2:


P%28r%5E2%2F4%29%2BPr%2BP Start with the expanded polynomial (from part a)



200%280.1%5E2%2F4%29%2B200%280.1%29%2B200 Plug in P=200 and r=0.1


200%280.01%2F4%29%2B200%280.1%29%2B200 Square 0.1 to get 0.01


200%280.0025%29%2B200%280.1%29%2B200 Divide


0.5%2B20%2B200 Multiply


220.5 Combine like terms.



So using either method, we get $220.5