A:

Interest is the cost of borrowing money, where the borrower pays a fee to the lender for using the latter’s money. The interest, typically expressed as a percentage, can be either simple or compounded. Simple interest is based on the principal amount of a loan or deposit, while compound interest is based on the principal amount and the interest that accumulates on it in every period. Since simple interest is calculated only on the principal amount of a loan or deposit, it’s easier to determine than compound interest.

Simple Interest

Simple interest is calculated using the following formula:

Simple Interest = Principal amount (P) x Interest Rate (I) x Term of loan or deposit (N) in years.

Generally, simple interest paid or received over a certain period is a fixed percentage of the principal amount that was borrowed or lent. For example, say a student obtains a simple-interest loan to pay one year of her college tuition, which costs $18,000, and the annual interest rate on her loan is 6%. She repays her loan over three years. The amount of simple interest she pays $3,240 ($18,000 x 0.06 x 3). The total amount she repays is $21,240 ($18,000 + $3,240).

Real-Life Simple Interest Loans

Two good examples of simple interest loans are auto loans and the interest owed on lines of credit such as credit cards.

A person could take out a simple interest car loan, for example. If the car cost a total of $100, to finance it the buyer would need to take out a loan with a $100 principal, and the stipulation could be that the loan has an annual interest rate of 5% and must be paid back in one year. Therefore, the simple interest on the car loan can be calculated as follows:

($100) x (5%) x (1)  = $5

Alternately, say an individual has a credit card with a $1,000 limit and a 20% APR. If, for example, he buys $1,000 worth of goods. He pays only the minimum the next month, $100. So the next month, with a $900 balance remaining, he would owe the following:

($900) x (20%) x (1)  = $180

Compound Interest

Conversely, compound interest accrues on the principal amount and the accumulated interest of previous periods; it includes interest on interest, in other words. It is calculated by multiplying the principal amount by the annual interest rate raised to the number of compound periods, and then minus the reduction in the principal for that year. Or as a formula:

Compound Interest = Total amount of Principal and Interest in future less Principal amount at present

To demonstrate, let’s go back to our student in the first example: She’s borrowing the same amount ($18,000) for college and repaying over the same three years, only this time it’s a compound-interest loan. The amount of compound interest that would be paid is $18,000 x (1.06)3 – 1) = $3,438.29 – obviously, higher than the simple interest of $3,240.

Examples of Simple and Compound Interest

Let’s run through a few examples to demonstrate the formulas for both type of interest.

Example 1: Suppose you plunk $5,000 into a one-year certificate of deposit (CD) that pays simple interest at 3% per annum. The interest you earn after one year would be $150: $5,000 x 3% x 1.

Example 2: Continuing with the above example, suppose your certificate of deposit is cashable at any time, with interest payable to you on a pro-rated basis. If you cash the CD after four months, how muc…