# 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.

## 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: