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Mary made a deposit of 600 dollars into a bank account at 5.5% compounded daily. How long (in years) will it take the 600 to accumulate to $789.90204?

I found the answer of this question to be 5 years.

Part b asks: How much interest is earned over the investment period?

Would that just be the Final value minus initial value? So 789.90204 - 600.

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  • $\begingroup$ Yes that is correct. $\endgroup$ – Attack68 Jun 26 '18 at 21:27
  • $\begingroup$ This was a question in our midterm paper, which was worth 25% of the whole grade. It seemed way too easy of a question, which worried me. THank you $\endgroup$ – Canadian Bacon Jun 26 '18 at 21:38
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$P = 600e^{.0001507t}$

$789.90 = 600e^{.0001507t}$

$.0001507t = \ln(\frac{789.90}{600})$

$$t = \frac{\ln(\frac{789.90}{600})}{.0001507}$$

$$t = 1825 \ \text{days} = 5 \ \text{years}$$

Just checking you were correct and yes, interest is $789.90 - 600$ = $\$189.90$

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