Economics

Correlation

Simple Interest

$$F=P+I$$

$$I=Pin$$

Simple Discount

$$D=fdn$$

$$d=\frac{i}{1+i}$$

Banker’s Year

1 year = 360 days

Exact Year

1 year =366 Days

Compound Interest

$$F=P\left(1+\frac{r}{m}\right)^{mn}$$

$$\left(i+\frac{r}{m}\right)=\left(1+ie\right)$$

Ordinary Annuity

$F=A\left(\frac{\left(1+i\right)^{n}-1}{i}\right)$ → Future Worth

$P=A\left(\frac{1}{i}-\frac{1}{i\left(1+i\right)^{n}}\right)=A\left(\frac{1-\left(1+\frac{r}{m}\right)^{-mn}}{i}\right)$ → Present Worth

$$A\sum_{LL}^{UL}\left(\left(1+\frac{r}{m}\right)^{x}\right)$$

LL = Period Covered - Last Annuity
UL = Period Covered - First Annuity

Annuity Due

$F=A\left(\frac{\left(1+i\right)^{n}-1}{i}\right)\left(1+i\right)$ → Future Worth

$P=A\left(\frac{1-\left(1+i\right)^{-n}}{i}\right)\left(1+i\right)$ → Present Worth

$$A\sum_{LL}^{UL}\left(\left(1+i\right)^{x}\right)$$

LL = (Period Covered - Last Annuity) + 1
UL = Period Covered - First Annuity

Deferred Annuity

$$P=\frac{A\left(\frac{\left(1+i\right)^{n}-1}{i\left(1+i\right)^{n}}\right)}{\left(1+i\right)^{n}}$$

Perpetual Annuity

$$P=\frac{A}{i}$$

Depreciation Methods

1. Straight Line Method

2. Sinking Fund

3. Sum of the Year’s Digit

4. Declining Balance

5. Double Declining balance

Straight Line Method

$$BV_{n}=FC-D_{n}$$

$$D=\frac{FC-SV}{n}$$

Sinking Fund Method

$$BV=FC-D$$

$$D=\frac{\left(FC-SV\right)i}{\left(1-i\right)^{n}-1}$$

Sum of the years digits method

$$AnnualDep=\frac{RemainingLife}{SumOfDigits}\left(FC-SV\right)$$

Declining balance Method

$$D=BV\left(Rate\right)$$

$$Rate=\frac{150\%}{Useful\,\;Life}$$

Double Declining Balance

$$D=BV\left(Rate\right)$$

$$Rate=\frac{200\%}{Useful\:Life}$$

Capitalized Cost

$$Present\:Worth+\frac{A}{i}+\sum_1^{999}\frac{InitialCost}{\left(1+i\right)^{mx}}$$