## Simple Interest vs. Compound Interest: An Overview

When analyzing the terms of a loan, it is important to consider more than the interest rate. Two loans can have identical principal amounts, interest rates, and repayment lengths but significant differences in the amount of interest you pay, especially if one loan uses simple interest and the other uses compound interest.

### Key Takeaways

- Simple interest is calculated by using only the principal balance of the loan each period.
- With compound interest, the interest per period is based on the principal balance
*plus*any outstanding interest already accrued. Interest compounds over time. - The Truth in Lending Act (TILA) requires that lenders disclose loan terms to potential borrowers, including the total dollar amount of interest to be repaid over the life of the loan and whether interest accrues simply or is compounded.

## Simple Interest

Simple interest is calculated using only the principal balance of the loan. 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 their college tuition, which costs $18,000, and the annual interest rate on their loan is 6%. They repay their loan over three years.

The Truth in Lending Act (TILA) requires that lenders disclose loan terms to potential borrowers, including the total dollar amount of interest to be repaid over the life of the loan and whether interest accrues simply or is compounded.

## Compound Interest

With compound interest, the interest per period is based on the principal balance plus any outstanding interest already accrued. Interest compounds over time. When calculating compound interest, the number of compounding periods makes a significant difference. Generally, the higher the number of compounding periods, the greater the amount of compound interest. So for every $100 of a loan over a certain period, the amount of interest accrued at 10% annually will be lower than the interest accrued at 5% semi-annually, which will, in turn, be lower than the interest accrued at 2.5% quarterly.

Besides scrutinizing the *Truth in Lending* statement, a quick mathematical calculation tells you whether you are looking at simple or compound interest.

### 72

Compound interest leads to the "Rule of 72", a quick, useful formula that is popularly used to estimate the number of years required to double the invested money at a given annual rate of return.

## Key Differences

Suppose you borrow $10,000 at a 10% annual interest rate with the principal and interest due as a lump sum in three years. Using a simple interest calculation, 10% of the principal balance gets added to your repayment amount during each of the three years. That comes out to $1,000 per year, which totals $3,000 in interest over the life of the loan. At repayment, then, the amount due is $13,000.

Now suppose you take out the same loan, with the same terms, but the interest is compounded annually. In the first year, the interest rate of 10% is calculated only from the $10,000 principal. Once that is done, the total outstanding balance, principal plus interest, is $11,000. The difference kicks in during the second year. The interest for that year is based on the full $11,000 that you currently owe, rather than just the $10,000 principal balance. At the end of year two, you owe $12,100, which becomes the base for the third-year interest calculation. When the loan is due, instead of owing $13,000, you end up owing $13,310. While you may not consider $310 a huge difference, this example is only a three-year loan; compound interest piles up and becomes oppressive with longer loan terms.

Another factor to watch for is how often interest is compounded. In the above example, it is once per year. However, if it is compounded more frequently, such as semi-annually, quarterly or monthly, the difference between compound and simple interest increases. More frequent compounding means the base from which new interest charges are calculated increases more rapidly.

One more simple method to determine if your loan uses simple or compound interest is to compare its interest rate to its annual percentage rate, which the TILA also requires lenders to disclose. The annual percentage rate (APR) converts the finance charges of your loan, which include all interest and fees, to a simple interest rate. A substantial difference between the interest rate and the APR means one or both of two things: your loan uses compound interest or it includes hefty loan fees in addition to interest.

## The Bottom Line

In real life situations, compound interest is often a factor in business transactions, investments, and financial products intended to extend for multiple periods or years. Simple interest is mainly used for easy calculations: those generally for a single period or less than a year, though they also apply to open-ended situations, such as credit card balances.

Get the magic of compounding working for you by investing regularly and increasing the frequency of your loan repayments. Familiarizing yourself with the basic concepts of simple and compound interest will help you make better financial decisions, saving you thousands of dollars and boosting your net worth over time.