## Interest

Interest is the cost of borrowing money or, alternatively, the compensation for the service and risk of lending money. In other words, interest is the amount paid on top of the original amount borrowed or invested (the principal). The rate of interest is typically expressed as an annual percentage of the principal.

There are two main types of interest:

**Simple Interest:**This is calculated only on the initial amount (principal) that was deposited or borrowed. The formula for simple interest is I = PRT, where I is the interest, P is the principal amount, R is the rate of interest, and T is the time in years.**Compound Interest:**This is calculated on the initial amount (principal) and also on the accumulated interest of previous periods. It’s often said that “interest earns interest” in the case of compound interest. Compound interest can significantly increase the amount of money over time, and it’s commonly used in real-world applications like savings accounts, loans, and investments.

Interest is a key concept in finance and it plays a crucial role in many areas, including banking, investing, and personal finance. When you borrow money, you pay interest, and when you lend or invest money, you can earn interest. The rate of interest is determined by a variety of factors, including the supply and demand of money in the economy, the creditworthiness of the borrower, and the expected inflation rate.

## Example of Interest

An example for both simple and compound interest.

**Simple Interest:**

Let’s say you invest $1,000 in a savings account that pays 5% simple annual interest for 3 years. Using the formula I = PRT:

- I is the interest
- P is the principal amount ($1,000)
- R is the rate of interest (5%, or 0.05 as a decimal)
- T is the time in years (3)

Plug the numbers in to get: I = $1,000 * 0.05 * 3 = $150

So, after 3 years, you would earn $150 in interest. Your total balance would be $1,150 (the original $1,000 plus $150 in interest).

**Compound Interest:**

Now, let’s say you put that same $1,000 in a different account that also has a 5% annual interest rate, but this one compounds annually for 3 years.

In this case, you would use the formula for compound interest: A = P(1 + r/n)^(nt)

- A is the amount of money accumulated after n years, including interest.
- P is the principal amount ($1,000).
- r is the annual interest rate (decimal) (5%, or 0.05 as a decimal).
- n is the number of times that interest is compounded per unit t.
- t is the time the money is invested for in years (3).

In this case, interest is compounded once per year, so n = 1. Plug the numbers in to get:

A = $1,000(1 + 0.05/1)^(1*3) = $1,000(1 + 0.05)^(3) = $1,000 * 1.05^3 ≈ $1,157.63

So, with compound interest, you would earn about $157.63 in interest over 3 years, for a total balance of $1,157.63. This is slightly more than with simple interest, because each year you’re earning interest on both the original amount and the interest you’ve already earned.