Simple & Compound Interest

Principal: The amount of money borrowed or invested.

Interest: The extra amount paid to the lender or investor.

Interest Rate (%): The extra amount paid to the lender or investor in percentage. It is usually calculated yearly (per annum) and sometimes monthly (per month).

$$Interest\;Rate\;per\;Annum = Interest\;Rate\;per\;Month \times 12$$

There are 2 types of interest calculation:

• Simple (Flat) Interest: The interest is calculated based on the original principal amount only.
• Compound Interest: The interest is calculated based on the accumulated prinicpal amount.

Simple Interest

$$\begin{align} Interest & = Principal \times Interest\;Rate \\ & = \frac{pr}{100} \\ \end{align}$$

$$\begin{align} Total\;Interest & = Principal \times Interest\;Rate \times Duration \\ & = \frac{prt}{100} \\ \end{align}$$

$$\begin{align} Total\;Amount & = Principal + Total\;Interest \\ & = Principal + \left( Principal \times Interest\;Rate \times Duration \right) \\ & = Principal \left( 1 + Interest\;Rate \times Duration \right) \\ & = p \left( 1 + \frac{rt}{100} \right) \\ \end{align}$$


Compound Interest

$$\begin{align} Total\;Amount\;in\;1st\;year, A_1 & = Principal \left( 1 + Interest\;Rate\;per\;annum \right) \\ Total\;Amount\;in\;2nd\;year, A_2 & = A_1 \left( 1 + Interest\;Rate\;per\;annum \right) \\ & = Principal \left( 1 + Interest\;Rate\;per\;annum \right)^2 \\ Total\;Amount\;in\;3rd\;year, A_3 & = A_2 \left( 1 + Interest\;Rate\;per\;annum \right)\\ & = Principal \left( 1 + Interest\;Rate\;per\;annum \right)^3 \\ & \vdots \\ Total\;Amount\;in\;nth\;year, A_n & = A_{n-1} \left( 1 + Interest\;Rate\;per\;annum \right) \\ & = Principal \left( 1 + Interest\;Rate\;per\;annum \right)^n \\ & = p \left( 1 + \frac{r}{100} \right)^n \\ \end{align}$$

$$Total\;Interest = Total\;Amount - Principal$$

Note: Compound interest is like calculating simple interest every year/month with a new (accumulated) principal.