document.write( "Question 1115217: dani invests 200 dollars at a rate of y% per year compound interest. at the end of 10 years the value of her investment is 256 dollars. Calculate the value of y, correct to 1 decimal place \n" ); document.write( "
Algebra.Com's Answer #730118 by addingup(3677)\"\" \"About 
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investment $200
\n" ); document.write( "rate of y% per year
\n" ); document.write( "compound annually
\n" ); document.write( "10 years
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\n" ); document.write( "200(1+y)^10 = 256
\n" ); document.write( "Let's divide both sides by 200 and we end up with:
\n" ); document.write( "(1+y)^10 = 256/200 simplify the right side, divide the top/bottom by 8:
\n" ); document.write( "(1+y)^10 = 32/25
\n" ); document.write( "Now to get rid of the exponent I am going to raise both sides to the inverse of 10 (you can do it with square roots but I find this easier):
\n" ); document.write( "((1+y)^10)^1/10 = (32/25)^1/10
\n" ); document.write( "On the right, divide 32/25. On the left, the power and its inverse cancel one another and we get:
\n" ); document.write( "1+y = 1.28^(1/10)
\n" ); document.write( "Now, let's make life easy. 1/10 = 0.1:
\n" ); document.write( "1+y = 1.28^0.1
\n" ); document.write( "= 1+y = 1.025
\n" ); document.write( "subtract 1 from both sides:
\n" ); document.write( "y = 0.025
\n" ); document.write( "since you need percent: 0.025*100= 2.5%
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\n" ); document.write( "Check:
\n" ); document.write( "200(1+0.025)^10 = 256
\n" ); document.write( "= 200(1.28) = 256 multiply on the left and prove that it is CORRECT.
\n" ); document.write( "Happy learning,
\n" ); document.write( "John
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