document.write( "Question 1085877: Deduce Compound rate of interest that will be required to produce $6,500 in 10yrs with initial deposit of $2,500. \n" ); document.write( "

Algebra.Com's Answer #699972 by jim_thompson5910(35256) $\"\"$ $\"About$

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FV = future value
\n" ); document.write( "PV = present value
\n" ); document.write( "r = interest rate
\n" ); document.write( "t = time in years
\n" ); document.write( "Note: I'm assuming the interest is compounded annually, so n = 1 which can be ignored in this case. For any other cases, then n would have to be included.\r
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\n" ); document.write( "\n" ); document.write( "In this case,
\n" ); document.write( "FV = 6500
\n" ); document.write( "PV = 2500
\n" ); document.write( "r = unknown (we're solving for it)
\n" ); document.write( "t = 10\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The formula we'll use is
\n" ); document.write( "FV = PV*(1+r)^t\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Plug in the given values. Solve for r
\n" ); document.write( "FV = PV*(1+r)^t
\n" ); document.write( "6500 = 2500*(1+r)^10
\n" ); document.write( "6500/2500 = (1+r)^10
\n" ); document.write( "2.6 = (1+r)^10
\n" ); document.write( "(2.6)^(1/10) = ((1+r)^10)^(1/10) ... raise both sides to the power 1/10
\n" ); document.write( "1.10026509310602 = 1+r
\n" ); document.write( "1.10026509310602-1 = r
\n" ); document.write( "0.100265093106018 = r
\n" ); document.write( "r = 0.100265093106018
\n" ); document.write( "Rounding to four decimal places, we get
\n" ); document.write( "r = 0.1003
\n" ); document.write( "Which converts to r = 10.03% when we move the decimal point 2 spots to the right.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The interest rate is approximately 10.03% \n" ); document.write( "

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