What Is Compound Interest?
Compound interest stands out due to its unique feature of not only being applied on the initial principal amount but also on the accumulated interest from previous periods. In simpler terms, compound interest involves earning or owing interest on the interest you have already earned. This characteristic sets it apart from simple interest, making it a powerful tool in the world of finance and investments.
The concept of compounding interest aids money to grow at a faster rate compared to calculations based solely on the principal sum. The more frequently interest is compounded, the greater the accelerated growth in compounded interest. For savers and investors, compound interest acts as a catalyst, multiplying their funds swiftly. Conversely, for individuals in debt, the compounding effect can make it challenging to pay off the interest owed.
Key Takeaways
- Compounding accelerates savings or debt.
- Compound interest involves both the initial principal and all previously accrued interest.
- Earning “interest on interest” defines the power of compound interest.
- Interest can compound at various frequencies, such as daily, monthly, quarterly, or annually.
- The more compounding periods, the greater the impact of compounding.
Investopedia / Julie Bang
How Compound Interest Works
Compound interest is computed by multiplying the initial principal amount by one plus the annual interest rate to the power of the number of compounding periods minus one. Subsequently, the total initial principal or loan amount is subtracted from the resulting value.
Katie Kerpel {Copyright} Investopedia, 2019.
The formula to calculate compound interest can be represented as:
- Compound interest = total future principal and interest (future value) – principal amount at present (present value)
= [P(1 + i)^n] – P
= P[(1 + i)^n – 1]
Where:
P = principal
i = annual interest rate
n = number of compounding periods
For instance, consider a 3-year loan of $10,000 at a 5% interest rate compounded annually. In this scenario, the interest amount would total $1,576.25:
$10,000[(1 + 0.05)^3 – 1] = $10,000 [1.157625 – 1] = $1,576.25
Another method for estimating compound interest is the Rule of 72. By dividing 72 by the rate of return, you can determine how long it will take for your money to double in value. For example, with a 4% return, $100 would grow to $200 in 18 years (72 / 4 = 18).
The Power of Compound Interest
Due to encompassing interest from prior periods, compound interest experiences an exponential growth rate. In the aforementioned example, although the total interest payable over three years is $1,576.25, this interest amount differs from what would result with simple interest. The interest payable at the end of each year is outlined in the table below.
Compound interest can significantly enhance investment returns over the long term. Over a span of 10 years, with a $100,000 deposit receiving 5% simple annual interest, the total interest earned would amount to $50,000. However, if the same deposit were subjected to a monthly compound interest rate of 5%, the interest accumulated would total around $64,700. While compound interest involves building interest on top of existing interest, cumulative interest reflects the sum of all interest payments.
Order your copy of Investopedia’s “What To Do With $10,000” magazine for more wealth-building advice.
Compounding Interest Periods
Compounding periods refer to the intervals at which interest is credited to the account. Interest can compound annually, semi-annually, quarterly, monthly, daily, continuously, or on varying schedules.
Interest may accrue daily in an account but only be credited monthly. It is crucial to note that interest starts compounding only once it is credited or added to the account balance, initiating the process of accruing additional interest. Different financial instruments adhere to standard compounding frequency schedules, such as:
- Savings accounts and money market accounts: Typically, savings accounts at banks compound interest daily.
- Certificate of deposit (CD): Common compounding frequencies for CDs include daily or monthly.
- Series I bonds: Interest is compounded semiannually, or every six months.
- Loans: Many loans compound interest monthly. However, in some cases, compounding interest may be referred to differently, such as “interest capitalization” for student loans.
- Credit cards: Credit card interest is often compounded daily, which can lead to rapid accumulation of interest charges.
Some banks offer continuously compounding interest, where interest is added to the principal as frequently as possible. Although it may not have a significant impact beyond daily compounding interest, it can be beneficial for quick deposits and withdrawals within the same day.
Compounding Period Frequency
More frequent compounding of interest favors the investor or creditor, while borrowers face the opposite effect. The fundamental rule dictates that a higher number of compounding periods results in greater compound interest accumulation.
The following table showcases the impact that different compounding periods can have on a $10,000 loan with a 10% annual interest rate over a 10-year timeframe.
Compound Interest: Start Saving Early
Young individuals often overlook retirement savings due to other immediate financial obligations. However, initiating savings at an early age can leverage compound interest, even with small amounts. Small contributions can lead to substantial returns over time, surpassing the benefits of saving larger sums later in life. Let’s explore the impact through an example.
Consider starting to save $100 monthly at age 20, achieving an average monthly compounded return of 4% over 40 years. By age 65, you would have earned $151,550, with just a $54,100 initial investment.
In contrast, if your twin starts investing at age 50 with an initial investment of $5,000 and then $500 monthly for 15 years with a similar 4% monthly compounded return, by age 65, they would have accrued only $132,147, despite investing $95,000.
When you reach the 45-year savings mark, while your twin would have saved for 15 years, your savings would surpass theirs, despite approximately double the principal investment made by your twin.
Similar principles apply to opening individual retirement accounts (IRAs) and utilizing employer-sponsored retirement accounts like 401(k) or 403(b) plans. Initiating savings early with consistent contributions maximizes the potential of compound interest accumulation.
Pros and Cons Compound Interest
Pros
-
Compound interest aids in long-term wealth building through investments and savings.
-
It mitigates risks of wealth erosion over time.
-
With proper management, compound interest can benefit consumers in loan repayments.
Cons
-
Minimum payments on high-interest loans or credit cards can lead to exponential growth in the debt balance due to compound interest.
-
Earnings from compound interest are taxable, impacting overall returns based on an individual’s tax bracket.
-
Calculating compound interest involves complexity compared to simple interest, often requiring specialized tools like online calculators.
Advantages Explained
- Compound interest fosters long-term wealth accumulation through investments and savings by allowing returns to generate further returns.
- It plays a crucial role in counteracting wealth depreciation resulting from factors like inflation, thus preserving purchasing power.
- By making payments above the minimum, individuals can optimize compound interest to reduce total interest costs.
Disadvantages Explained
- Minimum payments on high-interest loans or credit cards can lead to exponential debt growth through compound interest, trapping individuals in a debt cycle.
- Earnings from compound interest are taxable at an individual’s tax rate if not in a tax-advantaged account.
- Calculating compound interest requires complex formulas compared to simple interest, often necessitating the use of calculators for accurate computation.
Compound Interest in Investing
Investors utilizing brokerage account dividend reinvestment plans (DRIPs) leverage compound interest in their investment strategies.
Assets with dividends like dividend stocks or mutual funds provide an avenue for investors to tap into compound interest. Reinvesting dividends to acquire more shares of the asset facilitates further growth through additional interest.
Zero-coupon bonds offer investors another opportunity to benefit from compound interest. Traditional bond issues provide periodic interest payments, which, being paid out, do not compound. Conversely, zero-coupon bonds, purchased below their original value, grow over time utilizing compound interest to reach full maturity value.
Tools for Calculating Compound Interest
Various tools, like Microsoft Excel, offer assistance in computing compound interest through three different approaches:
Approach One: Multiplication
The initial method involves multiplying each year’s new balance by the interest rate.
For instance, depositing $1,000 into a savings account with a 5% annual compounding interest, and determining the balance after five years:
- In Excel, enter “Year” in cell A1, and “Balance” in cell B1.
- Insert years from 0 to 5 in cells A2 to A7.
- Initial balance at year 0 is $1,000, so enter “1000” in cell B2.
- In cell B3, input “=B2*1.05”.
- Continue this process till B7; in cell B7, calculate “=B6*1.05”.
- The computed value, $1,276.28 in cell B7, represents the account balance after five years.
Approach Two: Fixed Formula
Another method involves using a pre-defined formula for compound interest calculations.
The compound interest formula is ((P*(1+i)^n) – P), with P as the principal, i as the annual interest rate, and n as the number of periods.
- Using the previous financial scenario, input “Principal value” in cell A1 and “1000” in cell B1.
- Enter “Interest rate” in A2 and “.05” in B2.
- Input “Compound periods” in A3 and “5” in B3.
- Calculate compound interest in B4 using “= (B1*(1+B2)^B3)-B1”, resulting in $276.28.
Approach Three: Macro Function
A third method involves creating a macro function for compound interest calculations.
- Begin the Visual Basic Editor found in the developer tab.
- Choose “Module” under the Insert menu.
- Type “Function Compound_Interest (P As Double, I As Double, N As Double) As Double” on the first line.
- Enter “Compound_Interest = (P*(1+i)^n) – P” on the second line.
- Lastly, add “End Function” on the third line to complete the function.
- In the same Excel sheet as before, input “Compound interest” in cell A6 and write “=Compound_Interest(B1, B2, B3)” to obtain a value of $276.28 matching the earlier results.
Online