### 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.

### Simple Interest

Simple interest is calculated using only the principal balance of the loan.

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 off the principal balance plus any outstanding interest already accrued. Interest compounds over time.

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

### 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. 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 off 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.

### Key Takeaways

- Simple interest is calculated using only the principal balance of the loan.
- With compound interest, the interest per period is based off 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.