The Meek brothers are planning a trip around the world. They hope to work some as they go, but believe that they should have accessible $\$800$ per month so they can live in relative comfort for the year they plan to be gone. How much should they have in an account earning 6% compounded monthly when they leave so that they can withdraw the desired $800 each month for twelve months?
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Welcome to the Math Stack Exchange. What have you tried? By the way you might want to edit the question to make it more readable. – Paul Sundheim Feb 28 '15 at 22:01
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I have determined that the goal money is $9600 by doing $800/mo *12 mo. I'm not sure what to do next. – slor Feb 28 '15 at 22:16
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You'll never have $$9600$ sitting in one place at any instant in time, so writing this down as your "goal" may lead you in a wrong direction. – David K Feb 28 '15 at 22:22
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why don't you from the last month and work backwards? – abel Feb 28 '15 at 22:27
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i'm thinking $80012 then / (12.06) = 13333.33 – slor Feb 28 '15 at 22:30
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HINT: If the Meek brothers took out a $\$10,000$ mortgage from the bank to be paid off in $12$ equal monthly payments at $6\%$ interest compounded monthly, how much would each payment be?
That is a standard mortgage-payment calculation for which you can easily find a formula. This problem differs from the standard mortgage-payment problem in just two ways:
The bank is borrowing the money from the brothers, paying interest to them, and paying off the loan to them in installments rather than the other way around. That is, this is like a mortgage except that the brothers and the bank have swapped roles.
Usually you know the principal amount that is borrowed and you have to work out the monthly payments. Here you know the monthly payments and want to find the principal. But if you use the correct formula, you can solve it.
David K
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