q a 10

q a 10

course mth 172

im confused... this is simple and i will knock this out quick.

Good start; see my notes to clarify a couple of points.

Actually I regard this as the hardest of all the qa's. If you understand this then you understand something very close to the heart of calculus and the way it is applied.

im confused... this is simple and i will knock this out quick." " 1 `questionNumber 100000 Note that there are 11 questions in this assignment. `q001. Suppose that you expect for the next 6 years to receive a steady stream of extra income, at the rate of $20,000 per year. This income is expected to 'flow in' at a constant rate, day by day. Suppose furthermore that you expect that your money will grow at a constant annual rate of 8%. Assuming you do not use any of the money or interest, the question we want to answer is how much you would therefore expect to have at the end of 6 years. This problem is complicated by the fact that the money that goes in, say, today will earn interest over a longer period than the money you earn tomorrow. In fact, the money you receive in one minute will earn interest for a different length of time than the money you receive in a different minute. To begin to answer the problem you could start out by saying that while some of the money will earn interest for 6 years, some will go in at the very end of the 6-year period and will therefore not earn any interest at all, so the average time period for earning interest will be 3 years. You could then calculate the interest on the full amount for 3 years, and get a fairly good idea of the final amount. As we will see, you can't get a precise estimate this way, but it gives you a reasonable starting estimate. What would be the simple interest on the total 6-year amount of money flow for 3 years, and what would be the final amount?

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RESPONSE --> the simple interest = 20g x 3 = 60g 8% of that = 4800 60g + 4800 = 64800 =final amount i think.

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17:56:58 `questionNumber 100000 The total money flow would be $20,000 per year for 6 years, or $120,000. 8% simple interest for 3 years would be 3 * 8% = 24%, and 24% of $120,000 is $28,800, so your first estimate would be $28,800. You therefore expect to end up with something not too far from $148,800.

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RESPONSE --> but why do you figure in for 6 years when you said 3? i've done this before, this looks easy if u could go just a little more in depth, i know i would grasp it. nothing to spend a lot of time on.

The question was

'What would be the simple interest on the total 6-year amount of money flow for 3 years, and what would be the final amount?'

So we get the total amount of money flow for 6 years, which is $120,000.

We figure 3 years' interest on this amount because some will accumulate interest for pretty much the full 6 years, but some will accumulate interest for practically no time.

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18:06:43 `questionNumber 100000 `q002. Money usually doesn't earn simple interest. Interest is almost always compounded. If the interest on $120,000 was compounded annually at 8% for 3 years, what would be the final amount?

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RESPONSE --> 20g(1.08^3) = 25194.2?

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18:14:36 `questionNumber 100000 There is a more efficient way to calculate this, but we'll see that shortly. 8% of $120,000 is $9600, so after 1 year we will have $120,000 + $9600 = $129,600. Note that this result could have been obtained by multiplying $120,000 by 1.08. We will use this strategy for the next two years. After another year we will have $129,600 * 1.08 = $139,968. If you wish you can take 8% of $129,600 and add it to $129,600; you will still get $139,968. After a third year you will have $139,968 * 1.08 = $151,165. Note that this beats the $148,800 you calculated with simple interest. This is because each year the interest is applied to a greater amount than before; previously the interest was just applied to the starting amount.

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RESPONSE --> ok. i know i was using the wrong formula, i didn't account for that inital amount being added to itself. if it's 20g a year, it would have to almost double to get to that in half of 6 years. help?

If you did the entire $120,000 the same way you did the $20,000 you would get the same result. In other words, the correct result would be 6 times what you got.

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18:15:46 `questionNumber 100000 `q003. Money can earn interest that is compounded annually, quarterly, weekly, daily, hourly, or whatever. For given interest rate the maximum interest will be obtained if the money is compounded continuously. When initial principle P0 is compounded continuously at rate r for t interest periods (e.g., at rate 8% = .08 for t years), the amount at the end of the time is P = P0 * e^(r t). If the $120,000 was compounded continuously at 8% annual interest for 3 years, what would be the amount at the end of that period?

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RESPONSE --> ok, i will stop and send this. i will wrap this up later tonight or tommorrow.