Finding compound interest formula

[ChiralSuperfields]

Homework Statement

please see below

Relevant Equations

please see below

For this part (a),

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!

 

[Mark44]

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.

 

[Steve4Physics]

Edited.

Try this: https://www.khanacademy.org/economi...v/continuously-compounding-interest-formula-e