Difference between revisions of "Introduction to Finance"

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=== Growing Perpetuities ===
 
=== Growing Perpetuities ===
The amount of money that has to be invested at an interest rate of r, to yield a yearly rate return of C that grows by g every year is <math>PV = \frac{C}{r-g}.  Note that the first time a payment is made is one year after the investment.
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The amount of money that has to be invested at an interest rate of r, to yield a yearly rate return of C that grows by g every year is <math>PV = \frac{C}{r-g}</math>.  Note that the first time a payment is made is one year after the investment.

Revision as of 13:08, 12 August 2010

Definitions

Future Value

Compounding Factor for T Periods (Non continuous)

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 CF_T = (1+\frac{r}{m})^{mT}} where r is the annual interest rate, m is the number of time per year the rate is compounded, and T is the number of years that the rate is compounded.

Compounding Factor for T Periods (Continuous)

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 CF_T = e^{rt}} where r is the annual interest rate and T is the number of years that the rate is compounded.

Effective Annual Rate (Non continuous)

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 \hat{r} = (1+\frac{r}{m})^m - 1}

Effective Annual Rate (Continuous)

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 \hat{r} = e^r - 1}

Effective Monthly Rate (Non continuous)

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 \hat{r}_M = (1+\frac{r}{m})^{\frac{m}{12}} - 1}

Discounted Value

Discount Factor over T Periods

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 DF_T = \frac{1}{(1+r)^T}}

Present Value with constant R

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 PV = \sum_{t=1}^T \frac{C_t}{(1+r)^t}}

Perpetuities

Regular Perpetuities

The amount of money that has to be invested at an interest rate of r, to yield a constant yearly return of C is 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 PV = \frac{C}{r}} . Note that the first time C is paid out one year after the investment.

Deferred Perpetuities

The amount of money that has to be invested at an interest rate of r, to yield a constant yearly rate of return of C in t years from now is 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 PV = \frac{C}{r}*\frac{1}{(1+r)^t}} . Note that the first time C is paid out is in year t+1.

Growing Perpetuities

The amount of money that has to be invested at an interest rate of r, to yield a yearly rate return of C that grows by g every year is 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 PV = \frac{C}{r-g}} . Note that the first time a payment is made is one year after the investment.