document.write( "Question 165322This question is from textbook
\n" ); document.write( ": I ask this problem yesterday with no response.
\n" ); document.write( "A business invest $10,000 in a savings account for two years. At the beginning of the second year, an additional $3500 was invested. At the end of the second year, the account balance is $15,569.75. What is the interest rate? \n" ); document.write( "

Algebra.Com's Answer #121878 by Earlsdon(6294) $\"\"$ $\"About$

You can put this solution on YOUR website!
Your tutor must have taken the weekend off!
\n" ); document.write( "We'll use the formula for simple interest in this problem:
\n" ); document.write( " $\"A+=+P%281%2Bni%29\"$ Where A = the amount you will have after n years of P dollars invested at an interest rate of i per year (simple interest...not compounded).
\n" ); document.write( "Let's calculate the two amounts that you will have ( $\"A%5B1%5D\"$ ) and ( $\"A%5B2%5D\"$ ) from the two principal amounts invested ( $\"P%5B1%5D+=+10000\"$ for 2 years and $\"P%5B2%5D+=+3500\"$ for 1 year). You are told that the sum of these two equals $15,569.75
\n" ); document.write( " $\"A%5B1%5D+=+P%5B1%5D%281%2Bni%29\"$ Substitute: $\"P%5B1%5D+=+10000\"$ and $\"n+=+2\"$
\n" ); document.write( " $\"A%5B1%5D+=+10000%281%2B2i%29\"$ The amount at the end of 2 years from the $10,000.
\n" ); document.write( " $\"A%5B2%5D+=+P%5B2%5D%281%2Bni%29\"$ Substitute: $\"P%5B2%5D+=+3500\"$ and $\"n+=+1\"$
\n" ); document.write( " $\"A%5B2%5D+=+3500%281%2Bi%29\"$ The amount at the end of 2 years from the $3,500.
\n" ); document.write( " $\"A%5B1%5D%2BA%5B2%5D+=+15569.75\"$ The total amount at the end of two years. Substituting the $\"A%5B1%5D\"$ and $\"A%5B2%5D\"$ we get:
\n" ); document.write( " $\"10000%281%2B2i%29%2B3500%281%2Bi%29+=+15569.75\"$ Simplify.
\n" ); document.write( " $\"10000%2B20000i+%2B+3500%2B3500i+=+15569.75\"$ Combine like-terms.
\n" ); document.write( " $\"13500%2B23500i+=+15569.75\"$ Subtract 13500 from both sides.
\n" ); document.write( " $\"23500i+=+2069.75\"$ Divide both sides by 23500.
\n" ); document.write( " $\"i+=+0.08807\"$ Multiply by 100 to get the percent interest rate.
\n" ); document.write( "i = 8.807%
\n" ); document.write( "The interest rate is 8.807%
\n" ); document.write( "Check:
\n" ); document.write( " $\"A%5B1%5D+=+10000%281%2B2%280.08807%29%29\"$
\n" ); document.write( " $\"A%5B1%5D+=+10000%281.17614%29\"$
\n" ); document.write( " $\"A%5B1%5D+=+11761.4\"$
\n" ); document.write( " $\"A%5B2%5D+=+3500%281%2B0.08807%29\"$
\n" ); document.write( " $\"A%5B2%5D+=+3500%281.08807%29\"$
\n" ); document.write( " $\"A%5B2%5D+=+3808.245\"$
\n" ); document.write( " $\"A%5B1%5D%2BA%5B2%5D+=+11761.42%2B3808.245\"$
\n" ); document.write( " $\"A%5B1%5D%2BA%5B2%5D+=+15569.665\"$ Not quite equal to $15569.75 but very close! \n" ); document.write( "

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