# Simple vs. Compound – Health Now, Wealth Forever

By Gary, on February 4th, 2014

There are more than two ways to define interest charges on loans and saving or investment accounts.  But, the two that are the most common and agreed upon are “simple” and “compound” interest.  Each can can have variations but I will keep this post basic in nature.

You may or may not understand how to differentiate between the two and you may or may not care.  But, if you don’t and you do, here are the definitions, the way to calculate them and, the reasons behind them.

### Definition of ‘Simple Interest‘

A quick method of calculating the interest charge on a loan. Simple interest is determined by multiplying the interest rate by the principal by the number of periods.

Where: P is the loan amount I is the interest rate

N is the duration of the loan, using number of periods

Example:

The Loan Amount = \$25,000

The Annual Interest Rate = 3.5%

The Number of Years to Pay Off = 5

Simple Interest = \$25,000 x 0.035 x 60/12 = \$4,375

Therefore, to borrow \$25,000 for five years at 3 ½% simple interest you would pay \$29,375 back to the lender five years from now.

### Definition of ‘Compound Interest’

Compound Interest is calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. Compound interest can be thought of as “interest on interest,” and will make a deposit or loan grow at a faster rate than simple interest, which is interest calculated only on the principal amount. The rate at which compound interest accrues depends on the frequency of compounding; the higher the number of compounding periods, the greater the compound interest. Thus, the amount of compound interest accrued on \$100 compounded at 10% annually will be lower than that on \$100 compounded at 5% semi-annually over the same time period. Compound interest is also known as compounding.

The formula for calculating compound interest is:

Compound Interest = Total amount of Principal and Interest in future (or Future Value) less Principal amount at present (or Present Value)

Compound Interest = [P (1 + i)n] – P

Where:

P is the loan amount I is the interest rate

N is the duration of the loan, using number of periods

Example:

The Loan Amount = \$25,000

The Annual Interest Rate = 3.5% (monthly accrual)

The Number of Years to Pay Off = 5

Compound Interest = [\$25,000 (1+0.00292)60] – \$25,000 = \$4,779.51.

Therefore, to borrow \$25,000 for five years at 3 ½% compound monthly interest you would pay \$29,779.51 back to the lender five years from now.

#### You can now see that simple interest benefits the borrower and compound interest benefits the lender.

While the magic of compounding has led to the apocryphal story of Albert Einstein supposedly calling it the eighth wonder of the world and/or man’s greatest invention, compounding can also work against consumers who have loans that carry very high interest rates, such as credit-card debt. A credit-card balance of \$20,000 carried at an interest rate of 20% (compounded monthly) would result in total compound interest of \$4,388 over one year or about \$365 per month.

A couple sites for helping with the formulas:  (You can play with these to see which type of interest would be to your advantage).

Simple Interest Calculator                            Compound Interest Calculator