document.write( "Question 1195246: The value of a house appreciated at the rate of 3.5% per annum. If its original value was sh.2,000,000 calculate the time it would take to appreciate to sh. 2,029,500 \n" ); document.write( "
Algebra.Com's Answer #827665 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( "1 + r is the growth factor.
\n" ); document.write( "n is the number o time periods.
\n" ); document.write( "in this problem, the equation becomes:
\n" ); document.write( "2,029,500 = 2,000,000 * 1.035 ^ n
\n" ); document.write( "divide both sides of the equation by 2,000,000 to get:
\n" ); document.write( "(2,029,500 / 2,000,000) = 1.035 ^ n
\n" ); document.write( "take the log of both sides of the equation to get:
\n" ); document.write( "log(2,029,500 / 2,000,000) = log(1.035 ^ n)
\n" ); document.write( "by log laws, this becomes:
\n" ); document.write( "log(2,029,500 / 2,000,000) = n * log(1.035)
\n" ); document.write( "solve for n to get:
\n" ); document.write( "log(2,029,500 / 2,000,000) / log(1.035) = n = .4256299268.
\n" ); document.write( "confirm by replacing n in the original equation to get:
\n" ); document.write( "f = 2,000,000 * 1.035 ^ .4256299268 = 2,029,500.
\n" ); document.write( "this confirms the value of n is correct.
\n" ); document.write( "your solution is that it would take .4256299268 years for 2,000,000 to becomes 2,029,500.
\n" ); document.write( "that's a little less than half a year.
\n" ); document.write( "for your information, the log law used was.
\n" ); document.write( "log(x ^ a) = a * log(x)
\n" ); document.write( "here's a reference.
\n" ); document.write( "https://www.andrews.edu/~calkins/math/webtexts/numb17.htm\r
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