Finding compound interest formula

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The discussion centers on the compound interest formula, specifically the confusion surrounding the base of the function. The correct formula for continuously compounded interest is A = P_0e^{rt}, where e is the base. The user initially proposed A(t) = 500 × 6.5^t, which is incorrect due to the misuse of the base. The importance of using e arises from the nature of continuous compounding, which is emphasized in many finance textbooks. The thread concludes with a suggestion to refer to educational resources for clarification on the topic.
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Homework Statement
please see below
Relevant Equations
please see below
For this part (a),
1686806444867.png

I got ##A(t) = 500 \times 6.5^t## where t is in years. Does someone please know whhy their function is to base e? Is it because the money is compounded continuously?

Many thanks!
 
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ChiralSuperfields said:
Homework Statement: please see below
Relevant Equations: please see below

For this part (a),
View attachment 327892
I got ##A(t) = 500 \times 6.5^t## where t is in years. Does someone please know whhy their function is to base e? Is it because the money is compounded continuously?
Yes, and because the formula for interest compounded continuously is defined as ##A = P_0e^{rt}##. Most textbooks that discuss compound interest and in particular, interest compounded continuously, will develop this formula.

I don't know how you came up with 6.5 as the base. Was it as simple as adding 1 and 5.5? That's wrong for several reasons.
 
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