I was reviewing continous interest formulas when something stumped me.(adsbygoogle = window.adsbygoogle || []).push({});

The accepted formula for continous interest is A=Pe^{rt}, and the proof of it is simple enough to understand.

However, my math book solves the formula in a different way. It starts with the standard model for growth rate, P=P_{0}e^{kt}, and than solves for k.

Example: Determine how much money will exist in an account if Ed deposits 1000$ in an account with 5% interest for 5 years.

Case 1:

A=Pe^{rt}

A=1000e^{(.05)(5)}

Case 2:

P=P_{0}e^{kt}

P=1000e^{kt}

Evaluate the amount at one year to solve for k.

1000(1.05)=1050

1050=1000e^{k(1)}

Solve for k.

1050/1000=e^{k(1)}

k=ln(1.05)

P=1000e^{ln(1.05)t}

The growth constants are different in both cases. What is the cause of this?

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# Continous Interest

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