Simple interest vs. compound interest

Simple interest and compound interest are two different ways to calculate interest owed or earned. Simple interest is calculated on the principal, or original amount borrowed. Compound interest is based on both principal and accrued interest. 

What you’ll learn:

• Most mortgages, student loans and auto loans charge simple interest.

• Simple interest typically results in lower total interest charged on a loan.

• Savings accounts typically compound the interest earned.

• Compound interest generally leads to more total interest accumulated in a savings account.

Simple interest means there’s no interest on interest. With a loan, a borrower wouldn’t pay interest on accrued interest. With savings or investments, an account holder wouldn’t earn interest on accrued interest.

Lending products that typically charge simple interest are car loans, student loans, personal loans and mortgages.

Simple interest is less common than compound interest for savings and investment accounts.

The formula for calculating simple interest is the principal amount of the loan (P) multiplied by the annual interest rate (R) and the loan term in years (N): 

P × R × N

As an example of simple interest, imagine having a car loan with a $40,000 principal and a 6% annual interest rate for a 6-year loan term. The formula to calculate the amount you’d pay in interest for this example would be:

$40,000 (principal) × 0.06 (6% annual interest rate) × 6 (years of the loan term) = $14,400 (interest)

For a loan, compound interest is the amount of money paid on the principal, or original loan amount, plus the accumulated interest. In terms of savings and investments, compound interest is the amount of money earned on what has been saved or invested, known as the principal, plus the accumulated interest. 

Lending products that may use compound interest include credit cards, student loans and personal loans. Among the savings and investment accounts that typically pay compound interest are savings accounts, certificates of deposit (CDs), bonds and money market accounts.

For compound interest, two additional concepts might be worth understanding: 

1. Compounding periods: For savings, compounding periods could be annual, semiannual, quarterly, monthly or daily. If all other factors are equal, the more frequent the compounding, the more money an account holder could earn.

2. Time value: The idea that an amount of money is worth more now than the same amount would be in the future. There’s no guarantee this is true, but the idea is based on three factors:

a. Money that someone holds now can be invested and earn interest.
b. Money promised in the future might never be received.
c. Inflation could reduce the buying power of money in the future.

The formula for calculating compound interest for a savings account includes a timing element (T), along with the same variables from simple interest calculations (principal, rate and loan term) is: 

P (1 + R/N)^NT

Here’s an example of determining compound interest using a savings account. Suppose the principal is $10,000, the annual percentage yield (APY) is 3%, the compounding period is annual (365 days) and the number of years is 10. 

10,000 (1 + 0.03/365)^(365 × 10) = $13,498.42

Without adding any money to the original $10,000, an account holder would wind up with $13,498.42.

Whether simple interest is better than compound interest depends on whether you’re a borrower or a saver and investor.

If you’re a borrower, simple interest typically is better because a borrower pays interest only on the principal and not on the accumulated interest. On the other hand, a borrower pays interest on the principal and accumulated interest if they have a compound interest loan.

So for the same loan with the same terms, a borrower should save money on a simple interest loan versus a compound interest loan. But what time of interest is charged is typically up to lenders.

Compound interest is typically better than simple interest for savers and investors. If a savings or investment account compounds the interest, the account holder earns interest on the principal as well as the accumulated interest. But if the account offers simple interest, someone earns interest only on the principal and not the accumulated interest.

Simple interest and compound interest are two ways to calculate interest. As a borrower or investor, you may not have the option to choose how interest is calculated. But knowing the difference between simple and compound interest can help you better plan and budget.

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