Determine (without solving the problem) the maximal interval in which the solution of the given initial value problem is guarant
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The <em>money</em> account is doubled at an<em> interest</em> rate of 5.2 % compunded quarterly, that is, under the model of <em>compound</em> interest in a time period of about 3.5 years.
<h3>How to determine the doubling time of money account</h3>
The <em>compound</em> interest takes into account the change of money deposited in time in contrast with the <em>simple</em> interest, which only takes the initial amount of money into account. Please notice that four quarters equals a year.
The <em>compound interest</em> formula is described below:
<em>C = C' · (1 + r/100)ⁿ</em> (1)
Where:
- r - Interest rate
- n - Number of periods
- C' - Initial money amount
- C - Current money amount
If we know that C = 2 · C' and r = 5.2, then the doubling time is:
n = /㏒ C/C'/㏒ (1 + r/100)
n = ㏒ 2/㏒ 1.052
n ≈ 13.674
The <em>money</em> account is doubled at an<em> interest</em> rate of 5.2 % compunded quarterly, that is, under the model of <em>compound</em> interest in a time period of about 3.5 years.
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