document.write( "Question 887043: May has $10,000 to invest for five years.
\n" ); document.write( "How much additional interest will she earn if the investment provides a 5% annual return, when compared to a 4.5% annual return.
\n" ); document.write( "How long will it take her $10,000 to double in value if it earns 5% annually? What annual rate has been earned if $1,000 grows into $4,000 in 20 years?
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #536324 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
f = p * (1+i)^n
\n" ); document.write( "that's the formula for future value of a present amount.
\n" ); document.write( "f is the future value
\n" ); document.write( "p is the present amount
\n" ); document.write( "i is the interest rate per time period
\n" ); document.write( "n is the number of time periods.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "10,000 invested for 5 years at 5% interest would be solved as follows:
\n" ); document.write( "p = 10,000
\n" ); document.write( "i = .05
\n" ); document.write( "n = 5
\n" ); document.write( "formula becomes:
\n" ); document.write( "f = 10,000 * (1.05)^5 = 12762.81563\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "10,000 invested for 5 years at 4.5% interest would be solved as follows:
\n" ); document.write( "p = 10,000
\n" ); document.write( "i = .045
\n" ); document.write( "n = 5
\n" ); document.write( "formula becomes:
\n" ); document.write( "f = 10,000 * (1.045)^5 = 12461.81938\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "the interest at 5% is equal to 12762.81563 - 10000 = 2762.81564
\n" ); document.write( "the interest at 4.5% is equal to 12461.81938 - 10000 = 2461.81938
\n" ); document.write( "the difference is equal to 2762.81564 - 2461.81938 = 300.9962485 which can be rounded to 301.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "to find out how long it takes for the money to double at 5%, the formula is the same except now you are solving for n.
\n" ); document.write( "the formula is f = p * (1+i)^n
\n" ); document.write( "the formula becomes:
\n" ); document.write( "20000 = 10000 * (1.05)^n
\n" ); document.write( "divide both sides of this equation by 10000 to get:
\n" ); document.write( "2 = 1 * (1.05)^n which is the same as 2 = 1.05^n
\n" ); document.write( "since the variable is in the exponent, you need to take the log of both sides of this equation to solve.
\n" ); document.write( "you get:
\n" ); document.write( "log(2) = log(1.05^n) which becomes log(2) = n*log(1.05)
\n" ); document.write( "divide both sides of this equation by log(1.05) to get log(2) / log(1.05) = n
\n" ); document.write( "solve for n to get n = 14.20669908
\n" ); document.write( "that's your solution.
\n" ); document.write( "confirm by replacing n in the original equation to get f = 10000 * (1.05)^14.20669908 which results in f = 20000.
\n" ); document.write( "your solution is confirmed.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "your equation remains the same for the last part of you problem.
\n" ); document.write( "f = p * (1+i)^n
\n" ); document.write( "you know f and you know p and you know n.
\n" ); document.write( "you have to solve for i.
\n" ); document.write( "the equation becomes:
\n" ); document.write( "4000 = 1000 * (1+i)^20
\n" ); document.write( "divide both sides of the equation by 1000 to get 4000/1000 = (1+i)^20 which becomes:
\n" ); document.write( "4 = (1+i)^20
\n" ); document.write( "take the 20th root of both sides of this equation to get:
\n" ); document.write( "4^(1/20) = 1+i
\n" ); document.write( "subtract 1 from both sides of this equation to get:
\n" ); document.write( "4^(1/20) - 1 = i
\n" ); document.write( "use your calculator to solve for i to get i = .0717734625
\n" ); document.write( "replace i with that in the original equation to get:
\n" ); document.write( "4000 = 1000 * (1.0717734625)^20 which becomes 4000 = 4000
\n" ); document.write( "this confirms the solution is correct.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );