document.write( "Question 315530: Some people look forward to retiring from work by the age of 65. Compare the amounts at age 65 that would result from making an annual deposit of $1000 starting at age 20, or from making an annual deposit of $3000 starting at age 50, to an RRSP that earns 6% interest per annum, compounded annually. What are the final amounts for both situations and state which one is more profitable.\r
\n" ); document.write( "\n" ); document.write( "I know how to get the answer the only thing I'm iffy about is the amount of years.
\n" ); document.write( "For Option 1, is it (65-20=45 years) of saving or 46 years? Same thing with Option 2, is it (65-50=15 years) or 16 years? I'd really appreciate it if someone could help me out. Thanks in advance. \n" ); document.write( "

Algebra.Com's Answer #225733 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "I may be using a different formula from the one you were taught but it will\r\n" );
document.write( "amount to the same, especially in the number of years.\r\n" );
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document.write( "Suppose we look first at the case of making an annual deposit of $1000 starting at age 20 and making the last deposit at age 64.\r\n" );
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document.write( "The $1000 deposit made at age 64 will have drawn interest for 1 year, and will be worth 1000(1.06)^1\r\n" );
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document.write( "The $1000 deposit made at age 63 will have drawn interest for 2 years, and will be worth 1000(1.06)^2\r\n" );
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document.write( "The $1000 deposit made at age 62 will have drawn interest for 3 years, and will be worth 1000(1.06)^3\r\n" );
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document.write( "... (We observe that the number of years the deposit has drawn interest is always 65 minus the age) ...\r\n" );
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document.write( "The $1000 deposit made at age 22 will have drawn interest for 43 years, and will\r\n" );
document.write( "be worth 1000(1.06)^43\r\n" );
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document.write( "The $1000 deposit made at age 21 will have drawn interest for 44 years, and will\r\n" );
document.write( "be worth 1000(1.06)^44  \r\n" );
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document.write( "The $1000 deposit made at age 20 will have drawn interest for 42 years, and will\r\n" );
document.write( "be worth 1000(1.06)^45\r\n" );
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document.write( "So we have the geometric series:\r\n" );
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document.write( "1000(1.06) + 1000(1.06)^2 + ... + 1000(1.06)^45 =\r\n" );
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document.write( "1000(1.06 + 1.06^2 + 1.06^3 + ... + 1.06^45)\r\n" );
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document.write( "So the series in the parentheses is:\r\n" );
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document.write( "Therefore 1000 times that is $225508.12, which is the amount\r\n" );
document.write( "at age 65.\r\n" );
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document.write( "Next we look first at the case of making an annual deposit of $3000 starting at age 50 and making the last deposit at age 64.\r\n" );
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document.write( "The $3000 deposit made at age 64 will have drawn interest for 1 year, and will be worth 3000(1.06)^1\r\n" );
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document.write( "The $3000 deposit made at age 63 will have drawn interest for 2 years, and will be worth 3000(1.06)^2\r\n" );
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document.write( "The $3000 deposit made at age 62 will have drawn interest for 3 years, and will be worth 3000(1.06)^3\r\n" );
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document.write( "... (We observe again that the number of years is always 65 minus the age) ...\r\n" );
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document.write( "The $3000 deposit made at age 52 will have drawn interest for 43 years, and will\r\n" );
document.write( "be worth 3000(1.06)^13\r\n" );
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document.write( "The $3000 deposit made at age 51 will have drawn interest for 44 years, and will\r\n" );
document.write( "be worth 3000(1.06)^14  \r\n" );
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document.write( "The $3000 deposit made at age 50 will have drawn interest for 42 years, and will\r\n" );
document.write( "be worth 3000(1.06)^15\r\n" );
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document.write( "So we have the geometric series:\r\n" );
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document.write( "3000(1.06) + 3000(1.06)^2 + ... + 3000(1.06)^15 =\r\n" );
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document.write( "3000(1.06 + 1.06^2 + 1.06^3 + ... + 1.06^15)\r\n" );
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document.write( "So the series in the parentheses is:\r\n" );
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document.write( "Therefore 3000 times that is $74017.58, which is the amount\r\n" );
document.write( "at age 65.\r\n" );
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document.write( "Edwin

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