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

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(75887) (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%
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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
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A(1) = P(1+(0.10/2))^(2*1)
A(1) = P(1.05)^2
A(1) = P(1.1025)
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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]
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If P=$200 and r=10% you get:
A(1) = 200[1 + 2*0.05 + (0.05)^2]
A(1) = $220.50
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Cheers,
Stan H.
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