document.write( "Question 1193474: How much should you invest each month in order to have $700,000 if your rate of return is 2.1% compounded monthly and you want to achieve your goal in 40 years?\r
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\n" ); document.write( "\n" ); document.write( "How much should you invest each month in order to have $700,000 if you want to achieve your goal in 20 years?\r
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\n" ); document.write( "\n" ); document.write( "If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years?\r
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Algebra.Com's Answer #848672 by ikleyn(52788)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "(a) How much should you invest each month in order to have $700,000 if your rate of return is 2.1% compounded monthly and you want to achieve your goal in 40 years?\r
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\n" ); document.write( "\n" ); document.write( "(b) How much should you invest each month in order to have $700,000 if you want to achieve your goal in 20 years?\r
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\n" ); document.write( "\n" ); document.write( "(c) If you deposit the amount you need to achieve your goal in 20 years, how much will your savings be worth after 10 years?
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\n" ); document.write( "\n" ); document.write( "        Calculations in the post by the tutor  @yurtman are  INCORRECT.\r
\n" ); document.write( "\n" ); document.write( "        It is why his numbers are absurdist.\r
\n" ); document.write( "\n" ); document.write( "        I came to bring a correct solution.\r
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\n" ); document.write( "\n" ); document.write( "        I will solve here parts  (a)  and  (b).   I do not like when many problems/questions are packed in one post.\r
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\n" ); document.write( "\n" ); document.write( "        By the way,  it contradicts to the rules of this forum.\r
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document.write( "             Part (a)\r\n" );
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document.write( "This problem is to determine the amount of monthly payments/deposits.\r\n" );
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document.write( "Since the problem does not specifies when the monthly payments are due, I will assume that \r\n" );
document.write( "the monthly payments are at the end of each month. Then it is a classic Ordinary Annuity saving plan. \r\n" );
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document.write( "The general formula to start (which is a PREREQUISITE and which you should know from your textbook) is \r\n" );
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document.write( "    FV = \"P%2A%28%28%281%2Br%29%5En-1%29%2Fr%29\",    \r\n" );
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document.write( "Here  FV is the future value of the account;  P is the monthly payment (deposit); \r\n" );
document.write( "r is the monthly effective rate presented as a decimal; \r\n" );
document.write( "n is the number of deposits (= the number of years multiplied by 12, in this case).\r\n" );
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document.write( "From this formula, you get for the monthly payment \r\n" );
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document.write( "    P = \"FV%2A%28r%2F%28%281%2Br%29%5En-1%29%29\".     (1)\r\n" );
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document.write( "Under the given conditions, FV = $700,000;  r = 0.021/12;  n = 40*12 = 480.  \r\n" );
document.write( "So, according to the formula (1), you get for the monthly payment \r\n" );
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document.write( "    P = \"700000%2A%28%28%280.021%2F12%29%29%2F%28%281%2B0.021%2F12%29%5E480-1%29%29\" =  $931.80  (rounded).\r\n" );
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document.write( "The interest is 700000 - 480*931.80 = 252,736  dollars.\r\n" );
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document.write( "Answer.  The necessary monthly deposit is $931.80.\r\n" );
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document.write( "         The interest is @252,736.\r\n" );
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document.write( "             Part (b)\r\n" );
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document.write( "Use the same formula (1) for the monthly payment \r\n" );
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document.write( "This time, your input data is FV = $700,000;  r = 0.021/12;  n = 20*12 = 240.  \r\n" );
document.write( "So, according to the formula (1), you get for the monthly payment \r\n" );
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document.write( "    P = \"700000%2A%28%28%280.021%2F12%29%29%2F%28%281%2B0.021%2F12%29%5E240-1%29%29\" =  $2349.43  (rounded).\r\n" );
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document.write( "Answer.  The necessary monthly deposit is $2349.43.\r\n" );
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\n" ); document.write( "\n" ); document.write( "On Ordinary Annuity saving plans,  see the lessons\r
\n" ); document.write( "\n" ); document.write( "    - Ordinary Annuity saving plans and geometric progressions\r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on Ordinary Annuity saving plans\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "The lessons contain  EVERYTHING  you need to know about this subject,  in clear and compact form.\r
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\n" ); document.write( "\n" ); document.write( "When you learn from these lessons,  you will be able to do similar calculations in semi-automatic mode.\r
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