Science:Math Exam Resources/Courses/MATH104/December 2015/Question 02 (a)
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Question 02 (a) |
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If $4000 dollars is invested in a bank account at an interest rate of 6% per year, compounded continuously, how long will it take in years for the balance to reach $20000 dollars? |
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? |
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. |
Hint 1 |
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Recall that the (non-continuous) compound interest formula is where
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Hint 2 |
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Make the substitution in the formula of hint 1 and recall that |
Hint 3 |
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For continuous compounding, we have after making the substitution suggested in hint 2. We recognize the limit as |
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.
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Solution |
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Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. The solution is a straightforward application of the continuous compound interest formula (these variables are defined in hint 1). We are given and and we seek the for which
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