PROFIT AND LOSS
P = Profit/Gain
L = Loss
CP = Cost price
SP = Selling price
MP = Marked price
D = Discount
$\displaystyle P=SP-CP$
$\displaystyle L=CP-SP$
$\displaystyle P\%=\frac{P\times 100}{CP}$
$\displaystyle L\%=\frac{L\times 100}{CP}$
$\displaystyle SP=\frac{100+P\%}{100}\times CP$
$\displaystyle SP=\frac{100-L\%}{100}\times CP$
$\displaystyle CP=\frac{100}{100+P\%}\times SP$
$\displaystyle CP=\frac{100}{100-L\%}\times SP$
$\displaystyle D=MP-SP$
$\displaystyle D\%=\frac{D\times 100}{MP}$
$\displaystyle MP=\frac{100}{100-D\%}\times SP$
$\displaystyle SP=\frac{100-D\%}{100}\times MP$
$\displaystyle CP=\frac{100-D\%}{100+P\%}\times MP$
$\displaystyle MP=\frac{100+P\%}{100-D\%}\times CP$
L = Loss
CP = Cost price
SP = Selling price
MP = Marked price
D = Discount
$\displaystyle P=SP-CP$
$\displaystyle L=CP-SP$
$\displaystyle P\%=\frac{P\times 100}{CP}$
$\displaystyle L\%=\frac{L\times 100}{CP}$
$\displaystyle SP=\frac{100+P\%}{100}\times CP$
$\displaystyle SP=\frac{100-L\%}{100}\times CP$
$\displaystyle CP=\frac{100}{100+P\%}\times SP$
$\displaystyle CP=\frac{100}{100-L\%}\times SP$
$\displaystyle D=MP-SP$
$\displaystyle D\%=\frac{D\times 100}{MP}$
$\displaystyle MP=\frac{100}{100-D\%}\times SP$
$\displaystyle SP=\frac{100-D\%}{100}\times MP$
$\displaystyle CP=\frac{100-D\%}{100+P\%}\times MP$
$\displaystyle MP=\frac{100+P\%}{100-D\%}\times CP$
SIMPLE INTEREST
P = Principal
n = Years
r = Rate of interest
Simple Interest, SI = Same amount of interest every year
$\displaystyle SI=\frac{Pnr}{100}$
Amount, A = Total amount including interest
$\displaystyle A=P+I$
$\displaystyle A=P\left ( 1+\frac{nr}{100} \right )$
n = Years
r = Rate of interest
Simple Interest, SI = Same amount of interest every year
$\displaystyle SI=\frac{Pnr}{100}$
Amount, A = Total amount including interest
$\displaystyle A=P+I$
$\displaystyle A=P\left ( 1+\frac{nr}{100} \right )$
COMPOUND INTEREST
P = Principal
n = Years
r = Rate of interest
Amount, A = Total amount including interest
Annually, $\displaystyle A=P\left ( 1+\frac{r}{100} \right )^{n}$
Half-yearly, $\displaystyle A=P\left ( 1+\frac{r}{100\times 2} \right )^{2n}$
Quarterly, $\displaystyle A=P\left ( 1+\frac{r}{100\times 4} \right )^{4n}$
Compound Interest, CI = Interest of one year is added to amount and new interest is calculated
$\displaystyle CI=A-P$
Example
P = 8000
n = 3 years
r = 15% per annum
Simple Interest
Compound Interest
n = Years
r = Rate of interest
Amount, A = Total amount including interest
Annually, $\displaystyle A=P\left ( 1+\frac{r}{100} \right )^{n}$
Half-yearly, $\displaystyle A=P\left ( 1+\frac{r}{100\times 2} \right )^{2n}$
Quarterly, $\displaystyle A=P\left ( 1+\frac{r}{100\times 4} \right )^{4n}$
Compound Interest, CI = Interest of one year is added to amount and new interest is calculated
$\displaystyle CI=A-P$
Example
P = 8000
n = 3 years
r = 15% per annum
Simple Interest
| Year | $\displaystyle I=\frac{Pnr}{100}$ | $\displaystyle A=P+I$ |
|---|---|---|
| 1st year | $\displaystyle I=\frac{8000\times 1\times 15}{100}=1200$ | $\displaystyle A=8000+1200=9200$ |
| 2nd year | $\displaystyle I=\frac{8000\times 1\times 15}{100}=1200$ | $\displaystyle A=9200+1200=10400$ |
| 3rd year | $\displaystyle I=\frac{8000\times 1\times 15}{100}=1200$ | $\displaystyle A=10400+1200=11600$ |
| Total | $\displaystyle SI=3600$ | $\displaystyle A=11600$ |
Compound Interest
| Year | $\displaystyle I=\frac{Pnr}{100}$ | $\displaystyle A=P+I$ |
|---|---|---|
| 1st year | $\displaystyle I=\frac{8000\times 1\times 15}{100}=1200$ | $\displaystyle A=8000+1200=9200$ |
| 2nd year | $\displaystyle I=\frac{9200\times 1\times 15}{100}=1380$ | $\displaystyle A=9200+1380=10580$ |
| 3rd year | $\displaystyle I=\frac{10580\times 1\times 15}{100}=1587$ | $\displaystyle A=10580+1587=12167$ |
| Total | $\displaystyle CI=4167$ | $\displaystyle A=12167$ |
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