# Simple and Compound Interest

#### Summary

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Interest is the extra money that a bank gives you for saving or depositing your money with them. Similarly, when anybody borrow money, they pay interest.

In a Simple interest, the interest is calculated on the same amount of money in each time period, and, therefore, the interest earned in each time period is the same.

If Principal(P), Rate of interest(R%) per annum and Time(T) then the simple interest is given by
S.I = $\frac{\text{PTR}}{\text{100}}$.

Compound Interest
Compound interest is calculated on the principal and the interest for the previous period. The principal amount  increases with every time period, as the interest payable is added to the principal. This means interest is not only earned on the principal, but also on the interest of the previous time periods. So that the compound interest calculated is more than the simple interest on the same amount of money deposited.

When interest is compounded, the total amount is calculated using the formula  A = P ( 1 + $\frac{\text{R}}{\text{100}}$)n

Interest is generally calculated on a yearly basis. Sometimes, it can be compounded more than once with in a year. It can be compounded half yearly, which means twice a year, or quarterly, which means four times a year.

The period for which interest is calculated is called the conversion period. At the end of the conversion period, the interest is added to the principal to get the new principal.

The formula to calculate the new rate of interest with respect to the conversion period is
Time period = number of years x  $\frac{\text{12}}{\text{Number of months in conversion period}}$

When interest is compounded half yearly, the interest rate will be half of the annual interest rate.
When interest is compounded half yearly, the time period will be doubled.

Applications of Compound Interest
The formula for compound interest can also be used in finding the growth rate of population, rate of increase of bacteria, rate of increase of land rates, etc.

### 1 . A sum of money is borrowed and paid back in 2 annual intallments

Present worth of Rs. P due in n years is given by
Present worth =
Therefore, Principal = (Present...

### 2 . the population of a city was 20000 in the year 1997.it increased at the rate of 5%p.a. find the population at the end of the year 2000

Solution: A = P(1+ R/100) N

Initial population of the city (P) = 20,000
Rate of increas...

### 3 . There is 60% increase in an amount in 6 years at simple interest

Let the principal be P = Rs x
Amount, A = P + 60% of Rs x
= x + (60/100)x
= x...

### 4 . The C.I on a certain sum for 2 years is Rs. 410

Given that SI in 2 years = Rs 400
? SI for 1 year = Rs 400/2 = Rs 200
Hence CI for 1 year = Rs 200
Given compound in...

### 5 . A milkman sold two of his buffaloes for rs20000each.

Given cost of buffaloes = Rs 20000 each
Gain on one buffalo = 5%
Recall selling price,

= Rs 21,000...