Whether putting money aside in savings or investments or taking out a loan to finance significant life expenditures, individuals will encounter interest payments many times throughout their lives.
Understanding whether that interest is simple or compound—as well as how often compound interest is compounded—is significant both for choosing the right investments and avoiding paying too much for a loan.
Defining Interest
Interest is a fee paid by one party to another to use the first party’s money. In the case of investments that accrue interest, the investor provides capital to a company that uses it to fund operations or growth. In return, the investor receives interest payments.
On the other side, an individual may take out a loan to purchase a car or home. In that case, the borrower pays interest on the loan to the lending institution. The interest accrued depends on the principal amount, the interest rate, and the length of time the loan or investment is outstanding. However, there can also be a significant difference in the total interest paid based on whether it is simple or compound interest.
How Compound Interest Works
Compound interest is paid on both the principal and the already accrued interest. Effectively, the interest accrued is added to the principal, and that new sum is what interest is calculated against during the next cycle. In the case of a debt, paying down the interest and a portion of the principal each cycle can help prevent the debt from growing.
Compound interest can lead to exponential growth over time, especially for long-term investments. On the other hand, compound interest can also be why some people struggle to get out of their debt burdens.
For instance, it is the reason why only paying the minimum payment on a credit card can lead to growing debt in the long term.
Examples of Compound Interest Accounts
- Savings accounts are the most common type of account that accrues compound interest. The interest earned on a savings account is typically compounded daily.
- Certificates of deposit (CDs) accrue compound interest and have a set period the money must remain on deposit. CDs typically have a fixed interest rate and a fixed term, meaning owners agree to keep their money in the CD for a certain period in exchange for a higher interest rate, which is typically compounded monthly.
- Money market accounts are similar to savings accounts but typically have higher interest rates. They are also likely to have more stringent requirements than savings accounts for maintaining a balance to receive that higher rate.
- Investment accounts, such as stocks, bonds, and mutual funds, can also accrue compound interest. However, the amount of interest earned on these investments will vary depending on the performance of the investments.
- Retirement accounts, such as 401(k)s and IRAs, can also accrue compound interest. These accounts may also offer tax advantages, such as deferring tax payments until the money is withdrawn.
It is important to note that not all accounts that accrue compound interest are created equal. The interest rate, term, and fees associated with each account can vary, as can requirements for maintaining a minimum balance and penalties for early withdrawals.
How Simple Interest Works
In the case of simple interest, only the investment or loan amount is considered when calculating interest. Any interest accrued on that principal is paid separately, and no interest is charged against accumulated interest.
Simple Interest Formula
Simple interest is calculated on the principal amount only. The interest is paid at regular intervals, such as monthly or annually.
The formula for simple interest is:
I = (P*R*T)/100
P = principal amount
R = interest rate
T = time in years
For example, if someone invested $100 at a simple interest rate of 5% for five years, they would end up with $125.
Compound Interest Formula
Compound interest is calculated on the principal amount and on any interest that has already been earned. This means the interest is compounded or added to the principal amount, at regular intervals.
The formula for compound interest is:
A = P(1 + r/n)^nt
P = principal amount
r = interest rate
n = number of times interest is compounded per year
t = time in years
Compound interest is a much more complicated formula to calculate than simple interest. For this reason, it is often helpful to use a compound interest rate calculator to understand the actual interest that will accrue over time.
The trickiest part of compound interest is the “n” in the formula. Interest can be compounded annually, quarterly, monthly, or even daily, and the more frequently it is calculated, the faster interest will accrue.
Examples of How Compound Interest Works Differently than Simple Interest
While most real-world encounters with interest are likely to involve compound interest, it can help to see some differences between simple and compound interest in real-world applications.
- Investment: If an individual invests $100 at 5% interest compounded annually, they will have $105 at the end of the first year, just as with simple interest. However, if they invest the same amount at 5% interest compounded monthly, they will have $105.12 at the end of the first year.
- Loan: If someone borrowed $10,000 at 5% interest compounded annually and made no payments on the principal, they would owe $10,500 at the end of the first year and $11,025 at the end of the second year. Compounded monthly, the debt would be $10,511.62 at the end of the first year and $11,049.41 at the end of the second year. In comparison, the same scenario using simple interest would only result in $11,000 in debt at the end of the second year.
- Savings account: A savings account with a balance of $1,000 and a 5% interest rate compounded annually would earn $50 in interest in the first year and $52.50 in the second year. However, if the interest rate is compounded monthly, $1,000 would earn $50.51 in interest in the first year and $54.43 in the second year. In contrast, that same $1,000 earning simple interest would earn a straight $50 annually.
Which is Better: Simple or Compound Interest?
Whether compound interest or simple interest is better depends on who pays the interest. Simple interest will always be a better deal for the person or entity paying it. For instance, a loan involving simple interest would save the borrower money in the long run. However, an investor would profit more from an investment that pays compound interest.
Summary
Ultimately, the critical difference between compound and simple interest is whether or not the interest is added to the remaining principal owed and then accrues its own interest. Most credit and investment products—including savings accounts—will use compound interest. However, it is still significant to know how often interest is being compounded, as the more frequently that calculation is made, the more interest will be paid.
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