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Interest is the amount earned on the principal. The amount invested is called the principal. A sum of money invested over a period of time at a rate of interest yields an interest.
Interest is of two types
The simple interest is calculated by the formula
$$I=\dfrac {P\times N\times R}{100}$$
where P is the principal amount or sum invested
N is the number of years invested for
and R is the rate of interest
The total amount = Principal + Interest
A = P + I
Example
A man invests a sum of ₹5000 in a chit fund. At the end of 2 years, calculated at a simple rate of interest of 2%, find the amount received by the man.
$$I=\dfrac {5000\times 2\times 2}{100}$$
I = 200
Therefore, at the end of two years the man receives
A = P + I = 5000 + 200 = 5200
Compound Interest
When the interest is compunded annually, the amount at the end of two years will be calculated using the formula
$$A=P\left( 1+\dfrac {R}{100}\right) ^{n}$$
The above problem yields the following -
A=5000\left( 1+\dfrac {2}{100}\right) ^{2} = 5202
Repeated Simple Interest
This is an alternative method to the compund interest formula.
First year.
$$I=\dfrac {5000\times 1\times 2}{100}$$
I = 100
Second year
Now the principal for the second year is the principal for the first year plus the interest calculated for the first year.
P = 5000 + 100 = 5100
$$I=\dfrac {5100\times 1\times 2}{100}$$
I = 102
Therefore, the amount at the end of two years is
A = 5000 + 100 + 102 = 5202
Note
The result of repeated simple interest is the same as that obtained by using the compound interest formula.
Ratio
The comparison of two quantities expressed as a fraction is called a ratio.
A ratio may or may not have units in the numerator and the denominator
Rate
Rate is the ratio of two quantities with units for the numerator and the denominator.
Proportion
It is a comparison between two ratios. It is true if the ratios compared are equivalent and false otherwise.
The proportion is true if the cross products are equal.
Concept | Example |
---|---|
Ratio | $$\dfrac {5}{9}$$ |
Rate | 600 miles per hour |
Proportion | $$\dfrac {10}{15}=\dfrac {18}{35}$$ |
Cross Product (Multiplication) | $$\dfrac {a}{b}=\dfrac {c}{d}$$ a x d = b x c
The product of means is equal to the product of exptremes. |