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Interest is the money paid for borrowing money from someone else. It is defined as the amount which is paid by a borrower to the person from whom amount is borrowed. This amount is paid as compensation to the owner. When an amount is borrowed, an interest is paid to the owner. Interest rate is determined by taking a percentage of principal and it is paid as a fee for a specified period of time.

Mainly, there are two types of interests as follows:
  • Simple Interest
  • Compound Interest

Suppose, there are two persons X and Y and X lends money to Y. In this case, 'Y' is borrower. So, 'Y' pays a fee to 'X' and this fee is called as interest. This is also called simple interest or flat rate.

Whenever money is borrowed, total amount is equal to principle amount plus interest. So, we can say that
Total repayments = (Principal + Interest)
Usually amount is paid back in regular installments either monthly or weekly.
  • Monthly payment amount = Principal + $\frac{\text{Interest}}{\text{Loan Period (T)}}$ in months.
  • Weekly payment amount = Principal + $\frac{\text{Interest}}{\text{Loan Period (T)}}$ in weeks.
When time 'T' is given in years, we convert time 'T' from years to months. To do this, we will multiply 'T' by 12, because there are 12 months in a year.

Simple Interest

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Simple interest is the money you earn by initially investing some amount.

Formula for calculating simple interest, rate, time and principal are given below:

SI = $\frac{\text{PRT}}{100}$

Principal (P) = $\frac{100 \times I}{R \times T}$

Rate (R) = $\frac{100 \times I}{P \times T}$

Time (T) = $\frac{100 \times I}{P \times R}$

where, P = Principal Amount
R = Interest rate
T = Time period
I = Simple Interest

According to these three parameters, a simple interest is determined as follows:

Solved Examples

Question 1: Find the interest on a deposit of $\$$550, earning 3.5% interest compounded semi annually for 5 years.
For calculating the interest semiannually, we must divide the interest rate by the number of interest periods.

The interest rate r, compounded semiannually is $\frac{0.035}{5}$ = 0.007

Number of payment periods 't' is 5 years x 2 interest periods = 10

To calculate the balance, the formula we use is B = P(1 + r)$^{t}$
B: Final balance

P: Principal
R: Rate of interest
T: Number of interest periods

B = 550(1 + 0.007)$^{10}$
B = 589.73

Therefore, the balance after 5 years is about $\$$589.73

Question 2: Find the principal value when, time = 3 years, interest = $\$$500 and rate = 3% per annum.
Time = 3 years
Interest = $\$$500
Rate = 3%

Formula to find principal is given below:

Principal (P) = $\frac{100 \times I}{R \times T}$

Plugging in the given values in the above formula, we get

$\frac{100 \times 500}{3 \times 3}$ = $\frac{50000}{9}$

= 5555.55

Therefore, for the given data, principal is $\$$5555.55

Compound Interest

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Compound interest depends on principal amount and past interest. Compound interest is basically used to get interest over the interest to earn some profit. Here, the word 'compound' stands for compounding interest and principal.

Compound interest is interest that is paid on principal as well on interest on any time of period. It is generally used when a person invests on something and wants to gain an amount or profit.

In compound interest, investment rate grows exponentially. Formula for calculating total amount is as follows:

Total amount = P(1 + ($\frac{R}{100}$))$^{n}$

Compound Interest = Total amount - Principal

Now, let us see how to solve compound interest problems:

Solved Example

Question: David deposited $\$$12550 at 17.5% interest rate for 2 years in manufacturing. Find the compound interest and total amount.
The formula to find total amount is as follows:
Total amount = P(1 + ($\frac{R}{100}$))$^{n}$

Given: P = 12550, R = 17.5%, n = 2

A = 12550(1 + ($\frac{17.5}{100}$))$^{2}$
   = 12550(1 + 0.175)$^{2}$
   = 17326.84

Total amount = $\$$17326.84

Compound interest = Total amount - Principal
= 17326.84 - 12550
= 4776.84

Compound interest = $\$$ 4776.84