Interest is the price for borrowing money. It is identified as a percentage of the principal amount borrowed over a specified period of time.

When it comes to loans and investments there are two types of interest: simple and compound.

Simple Interest

Simple interest is calculated on the original principal only and is often the easier of the two to calculate. The principal remains fixed throughout the loan and these loans are usually specified for shorter terms.

To calculate simple interest, this formula is used: I = prt

I = Interest, p = principal, r = rate, t = time periods

Example: You borrow $20,000 at 6% yearly interest for 3 years

I = $20,000 x 0.06 x 3 = $3600

If you borrow the same amount at the same rate but change the time period to 90 days, the calculation would be:

I = $20,000 x 0.06 x 0.25 (90 days/365 days) = $300

Note: The t in the equation must be in number of years, so 90 is divided by 365 days which equals 0.25 years.

Simple interest is very basic and often used to get a quick calculation of estimated interest on a particular loan or investment. Simple interest does not utilize any calculations of compounding interest.

Compound Interest

Lenders use compound interest when offering long-term loans. Compound interest is not only paid on the original principal as with simple interest, but it is also paid on past interest as well. In this type of loan, the principal changes as interest accumulates.

Compound interest is also used for investment purposes. Compounding interest on a savings account can equate to a large amount of savings and money accumulation. To see how much you can gain through making an investment use this compound interest calculator.

Calculating compound interest is more complex than simple interest. To calculate compound interest on a loan, you must take into account the original principal plus past accumulated interest.  Interest is often stated as a yearly rate; however, the compounding periods can vary.

Below is an example of how compounded interest is calculated and added year after year:

I = Prt

P = Principal, r = annual interest rate, t = years of loan, I = the money including interest accumulated after t years

Example: You are borrowing $200,000 at an annual interest rate of 5% for 3 years compounded annually.

(I¹) Interest Year 1 = p¹rt = $200,000 x 0.05 x 1 = $10,000

(I²) Interest Year 2 = p²rt (p² = p¹ + I¹ = $10,000 + $200,000 = $210,000)
$210,000 x 0.05 x 1 = $10,500

(I³) Interest Year 3 = p³rt (p³ = p² + I² = $210,000 + $10,500 = $220,500)
$220,500 x 0.05 x 1 = $11,025

For Interest year 1, designated by I¹, the principal is multiplied by the rate (r) and 1 year. For the interest for year 2 (I²), a new principal was formed by adding the original principal ($200,000) to the interest accumulated from year 1 ($10,000). This new principal ($210,000) is brought through the same basic calculation (I=prt). To calculate the interest for year 3, the new interest from year 2 ($10,500) must be added to the principal calculated in year 2 ($210,000) which equals $220,500. This new number is plugged into the same calculation to get the interest for year 3.

The total interest paid for 3 years in this example is: $10,000 + $10,500 + $11,025 = $31,525. As you can see from this example, compound interest grows faster than simple interest.

Compound Interest at a Glance

For a quick calculation of compound interest and to see what the total interest plus principal would equal over the life of a 15 year loan, use this calculation:

A= P(1+r)^n  where A is the total cost of mortgage including interest and n is the total number of years (15).

A = $200,000 (1 + 0.05)^15

Note: The ^15 designates “to the power of 15″. In this equation, you must multiply the value in the parentheses (1+0.05) by itself 15 times.

A = $200,000 (1.05) ^15
A = $200,000 x 2.079 = $415,800