# Simple and Compound Interest

## What is simple Interest?

**Simple interest** is a quick and easy method of calculating the **interest** charge on a loan. **Simple interest** is determined by multiplying the daily **interest** rate by the principal by the number of days that elapse between payments. Simple interest is not commonly used by the banking industry.

## I=prt

## Interest = principal amount x rate x time

## What is compound Interest?

Compound interest is calculated based on the principal, interest rate (APR or annual percentage rate), and the time involved:

**P** is the principal (the initial amount you borrow or deposit)

**r** is the annual rate of interest (percentage)

**n** is the number of years the amount is deposited or borrowed for.

**A** is the amount of money accumulated after n years, including interest.

When the interest is compounded once a year:

**A = P(1 + r) ^{n}**

However, if you borrow for 5 years the formula will look like:

**A = P(1 + r)**^{5}

This formula applies to both money invested and money borrowed.

### Frequent Compounding of Interest

What if interest is paid more frequently? It's not much more complicated, except the rate changes. Here are a few examples of the formula:

Annually = **P** × (1 + r) = (annual compounding)

Quarterly = **P** (1 + r/4)4 = (quarterly compounding)

Monthly = **P** (1 + r/12)12 = (monthly compounding)

### Compound Interest Table

Confused? It may help to examine a graph of how compound interest works. Say you start with $1000 and a 10% interest rate. If you were paying simple interest, you'd pay $1000 + 10%, which is another $100, for a total of $1100, if you paid at the end of the first year. At the end of 5 years, the total with simple interest would be $1500.

The amount you pay with compound interest depends on how quickly you pay off the loan. It's only $1100 at the end of the first year, but is up to over $1600 at 5 years. If you extend the time of the loan, the amount can grow quickly:

### Compound Interest Table

Confused? It may help to examine a graph of how compound interest works. Say you start with $1000 and a 10% interest rate. If you were paying simple interest, you'd pay $1000 + 10%, which is another $100, for a total of $1100, if you paid at the end of the first year. At the end of 5 years, the total with simple interest would be $1500.

The amount you pay with compound interest depends on how quickly you pay off the loan. It's only $1100 at the end of the first year, but is up to over $1600 at 5 years. If you extend the time of the loan, the amount can grow quickly: