document.write( "Question 1161158: 1) Find the future value of a simple interest loan of $4,000 at 5.5% interest for 7 months?
\n" ); document.write( "2) Find the present value of $26,500 in 9 months at 5.8% interest.
\n" ); document.write( "3) Find the time required for an investment of 5000 dollars to grow to 6400 dollars at an interest rate of 7.5 percent per year, compounded quarterly. \n" ); document.write( "
Algebra.Com's Answer #784672 by Theo(13342)\"\" \"About 
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1) Find the future value of a simple interest loan of $4,000 at 5.5% interest for 7 months?\r
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\n" ); document.write( "\n" ); document.write( "simple interest rate formula is f = p*(1+r*n)
\n" ); document.write( "f = future value
\n" ); document.write( "p = present value
\n" ); document.write( "r = interest rate per time period
\n" ); document.write( "n = number of time periods\r
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\n" ); document.write( "\n" ); document.write( "p = 4000
\n" ); document.write( "r = .055 per year
\n" ); document.write( "n = 7/12 years
\n" ); document.write( "f = 4000 * (1+.055*7/12) = 4018.3333333....
\n" ); document.write( "that's your future value.\r
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\n" ); document.write( "\n" ); document.write( "2) Find the present value of $26,500 in 9 months at 5.8% interest.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "simple interest rate formula is f = p*(1+r*n)
\n" ); document.write( "f = future value
\n" ); document.write( "p = present value
\n" ); document.write( "r = interest rate per time period
\n" ); document.write( "n = number of time periods\r
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\n" ); document.write( "\n" ); document.write( "f=26500
\n" ); document.write( "r=.058 per year
\n" ); document.write( "n=9/12 years
\n" ); document.write( "26500 = p*(1+058*9/12)
\n" ); document.write( "divide both sides of this formula by (1+058*9/12) to get:
\n" ); document.write( "26500/(1+1.058*9/12) = 25395.30426
\n" ); document.write( "that's your present value.\r
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\n" ); document.write( "\n" ); document.write( "3) Find the time required for an investment of 5000 dollars to grow to 6400 dollars at an interest rate of 7.5 percent per year, compounded quarterly.\r
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\n" ); document.write( "\n" ); document.write( "compound interest formula is f = p*(1+r)^n
\n" ); document.write( "f = future value
\n" ); document.write( "p = present value
\n" ); document.write( "r = interest rate per time period
\n" ); document.write( "n = number of time periods\r
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\n" ); document.write( "\n" ); document.write( "f = 6400
\n" ); document.write( "p = 5000
\n" ); document.write( "r = .075 per year divided by 4 = .07/12 per quarter.
\n" ); document.write( "n = number of quarters\r
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\n" ); document.write( "\n" ); document.write( "formula becomes:
\n" ); document.write( "6400 = 5000*(1+.075/4)^n
\n" ); document.write( "divide both sides of the formula by 5000 to get:
\n" ); document.write( "6400/5000 = (1+.075/4)^n
\n" ); document.write( "take the log of both sides of this equation to get:
\n" ); document.write( "log(6400/5000) = log((1+.075/4)^n)
\n" ); document.write( "by properties of logs, this becomes:
\n" ); document.write( "log(6400/5000) = n*log(1+.075/4)
\n" ); document.write( "solve for n to get:
\n" ); document.write( "n = log(6400/5000)/log(1+.075/4) = 13.28891872
\n" ); document.write( "confirm by replacing n in original equation to get:
\n" ); document.write( "f=5000*(1+.075/4)^13.28891872 = 6400.
\n" ); document.write( "this confirms the solution is correct.
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