Introduction to Finance

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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.

Annuities

Regular Annuities

The amount of money that has to be invested at an interest rate of r, to yield a constant yearly return of C for T years is given by 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}*(1-\frac{1}{(1+r)^T})} . Note that the first annuity is paid out one year from the date of the investment.

Growing Annuities

The amount of money that has to be invested at an interest rate of r, to yield a yearly return of C which grows by g each year for T years is given by 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}*(1-(\frac{1+g}{1+r})^T)} . Note that the first annuity is paid out one year from the date of the investment.

Interest Rate

Real Interest Rate

The real interest rate given the nominal interest rate r and the inflation rate i is given as 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=\frac{1+r}{1+i}-1}