Difference between revisions of "Math 22 Natural Exponential Functions"
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<math>\lim_{x\to 0} (1+x)^{\frac{1}{x}}=e</math> | <math>\lim_{x\to 0} (1+x)^{\frac{1}{x}}=e</math> | ||
<math>e\approx 2.71828182846</math> | <math>e\approx 2.71828182846</math> | ||
| + | |||
| + | ==Compound Interest== | ||
| + | Let <math>P</math> be the amount deposited, <math>t</math> the number of years, <math>A</math> the balance, and <math>r</math> the annual interest rate (in decimal form). | ||
| + | 1. Compounded <math>n</math> times per year: <math>A=P(1+\frac{r}{n})^{rt}</math> | ||
| + | 2. Compounded continuously: <math>A=Pe^{rt}</math> | ||
| + | |||
[[Math_22| '''Return to Topics Page''']] | [[Math_22| '''Return to Topics Page''']] | ||
'''This page were made by [[Contributors|Tri Phan]]''' | '''This page were made by [[Contributors|Tri Phan]]''' | ||
Revision as of 06:57, 11 August 2020
Limit Definition of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle e}
The irrational number Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle e}
is defined to be the limit:
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lim_{x\to 0} (1+x)^{\frac{1}{x}}=e}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle e\approx 2.71828182846}
Compound Interest
Let Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P}
be the amount deposited, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t}
the number of years, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A}
the balance, and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r}
the annual interest rate (in decimal form).
1. Compounded Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n}
times per year: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A=P(1+\frac{r}{n})^{rt}}
2. Compounded continuously: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A=Pe^{rt}}
This page were made by Tri Phan