# Interest

**Interest** is the amount of money a lender or financial institution receives for lending out money. Interest can also refer to the amount of ownership a stockholder has in a company, usually expressed as a percentage

The most common **types** are simple, compound, and continuous compound interest types. What's more, how the interest is calculated will also be variable, for example, whether it's changed or compiled on a daily, monthly, or yearly basis. Either way, the percentage will change.

**Interest payments** are the cost of borrowing money. The borrower makes these payments in addition to paying back the principal on a loan. If you lend money with interest, the interest payment is the amount you are paid over and above the principal amount you lent.

**Simple Interest **is calculated using the following formula: **SI = (P × R × T)/100**, where P = Principal, R = Rate of Interest, and T = Time period. Here, the rate is given in percentage (r%) is written as r/100.

### Compound Interest

The compound interest is obtained by subtracting the principal amount from the compound amount. Hence, the formula to find just the compound interest is as follows: **CI = P (1 + r/n) ^{nt} - P**.

In the above expression,

- P is the principal amount
- r is the rate of interest(decimal obtained by dividing rate by 100)
- n is the number of times the interest is compounded annually
- t is the overall tenure.

## Continuous Compounding

Instead of calculating interest on a finite number of periods, such as yearly or monthly, continuous compounding calculates interest assuming constant compounding over an infinite number of periods. The formula for compound interest over finite periods of time takes into account four variables:

- PV = the present value of the investment
- i = the stated interest rate
- n = the number of compounding periods
- t = the time in years

The formula for continuous compounding is derived from the formula for the future value of an interest-bearing investment:

Future Value (FV) = PV x [1 + (i / n)]^{(n x t)}

Calculating the limit of this formula as n approaches infinity (per the definition of continuous compounding) results in the formula for continuously compounded interest:

**FV = PV x e ^{(i x t)}**, where e is the mathematical constant approximated as 2.7183.