document.write( "Question 1189632: Mariel deposits Php 50,000 in a savings account. The account pays 6% annual interest. How many years will it take for her money to grow up to Php 89,542 \n" ); document.write( "
Algebra.Com's Answer #821056 by Theo(13342)\"\" \"About 
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f = p * (1 + r) ^ n
\n" ); document.write( "f is the future value
\n" ); document.write( "p is the present value
\n" ); document.write( "r is the interest rate per time period
\n" ); document.write( "n is the number of time periods.\r
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\n" ); document.write( "\n" ); document.write( "when the time periods are in years and the interest rate is 6% per year and the present value is 50,000 and the future value is 89,542, the formula becomes:\r
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\n" ); document.write( "\n" ); document.write( "89,542 = 50,000 * (1 + .06) ^ n
\n" ); document.write( "divide both sides of the equation by 50,000 and simplify the right side of the equation to get:
\n" ); document.write( "89,542/50,000 = 1.06 ^ n
\n" ); document.write( "take the log of both sides of the equation to get:
\n" ); document.write( "log(89,542/50,000) = log(1.06^n) which becomes:
\n" ); document.write( "log(89,542/50,000) = n*log(1.06)
\n" ); document.write( "divide both sides of the equation by log(1.06) to get
\n" ); document.write( "log(89,542/50,000)/log(1.06) = n
\n" ); document.write( "solve for n to get:
\n" ); document.write( "n = 9.999926243.
\n" ); document.write( "replace n in the original equation with that and solve for f to get:
\n" ); document.write( "f = 50,000 * 1.06^9.999926243 = 89,542.
\n" ); document.write( "this confirms the value of n is good.
\n" ); document.write( "your solution is that it will take 9.999926243 years for her money to grow to 89,542.
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