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Simple interest vs compound interest explained

explain the difference between simple interest and compound interest

Simple interest is a way of calculating the interest charge on a loan or investment based on the original principal amount and the interest rate. Compound interest, on the other hand, is calculated not just on the initial principal but also on the accumulated interest from previous periods. 

Simple interest is better for installment loans, while compound interest is preferable for investment accounts. In fact, the average savings account currently yields about 0.46% annual interest!

What Is Simple Interest?

Simple interest is the interest rate based on the principal balance of a loan or investment. Suppose you borrow money through a poor credit personal loan and repay through equal monthly installments. Those monthly payments consist of the principal balance and the interest fee. 

A standard interest rate does not change over time. This means a borrower always pays the same amount of money for loan payments. An example of a simple interest loan is a debt consolidation loan, which typically has a 7% rate or lower!2

Pros of Simple Interest

  • Borrowers benefit from predictable and often lower total interest payments over the life of a loan. 
  • Individuals with fixed-income investments receive a steady return over the investment period.

Cons of Simple Interest

  • Savers and investors may earn less over time as interest is not compounded.
  • Lenders and financial institutions might receive lower returns on their lending products compared to those with compound interest.

How To Calculate Simple Interest

To calculate simple interest, you must use the simple interest formula I = (P x R x T). Calculating simple interest is easy, but you need to know the following information:

  • I is the interest amount
  • P is the principal amount (the initial sum of money)
  • R is the annual interest rate (in decimal form)
  • T is the time the money is invested or borrowed for (in years)

To find the total amount owed or accumulated after the interest is applied, you simply add the interest (I) to the principal (P). For example, if you invest $1,000 (the principal) at a simple interest rate of 5% per year (0.05 in decimal) for 3 years, the interest would be $1,000 \times 0.05 \times 3 = $150. So, the total amount after 3 years would be $1,150.

What Is Compound Interest? 

Compound interest is a type of interest rate that combines the principal amount with the total accumulated interest. Money can be compounded daily, monthly, or yearly. 

Compound interest can be exceedingly beneficial when you invest because you can quickly grow your money. Most savings accounts have compound interest. Compound interest examples include money market accounts and certificates of deposit (CD). Ideally, your financial investment should compound as frequently as possible. 

Pros of Compound Interest

  • Savers and investors can significantly increase their savings, especially over long periods.
  • Financial institutions offering compound interest products can attract more customers seeking to grow their investments.

Cons of Compound Interest

  • Outstanding debt can grow quickly due to the compounding effect.
  • Investors might underestimate the amount of interest to be paid on loans or the growth of investments.

How To Calculate Compound Interest

The formula for calculating compound interest is: A = P (1 + [r / n]) ^ nt. If you want to calculate compound interest, you will need to know the following information.  

  • A = The amount of money accumulated after N years, including interest.
  • P = Principal amount
  • R = Annual rate of interest (as a decimal)
  • N = The number of times that interest is compounded per year
  • T = How long money is deposited or borrowed (in years)

Here’s how to use the compound interest formula:

  1. Divide the annual interest rate by the number of compounding periods per year.
  2. Add 1 to the result from step 1.
  3. Raise the result from step 2 to the power of the total number of compounding periods (compounding frequency times the number of years).
  4. Multiply the principal amount by the result from step 3 to get the total accumulated amount.
  5. Subtract the principal from the total accumulated amount to find the compound interest earned.

For example, if you invest $1,000 at an annual rate of 5% compounded annually for 3 years, the calculation would be A = $1,000 \times (1 + \frac{0.05}{1})^{1 \times 3}, which simplifies to A = $1,000 \times (1.05)^3, and the total accumulated amount would be approximately $1,157.63. The compound interest earned would be $157.63.

Simple Interest vs. Compound Interest 

Simple interest and compound interest differ significantly. Take a look at an example below:

DescriptionSimple Interest CalculationCompound Interest Calculation
Principal (P)$1,000$1,000
Annual Interest Rate (r)5% (or 0.05)5% (or 0.05)
Time (t)3 years3 years
Compounding Frequency (n)N/A (simple interest does not compound)Annually
Interest Earned (I or A-P)I = P * r * t = $1,000 * 0.05 * 3 = $150A = P * (1 + r/n)^(nt) – P = $1,000 * (1 + 0.05/1)^(1*3) – $1,000 = $157.63
Total Amount (A)A = P + I = $1,000 + $150 = $1,150A = $1,000 * (1 + 0.05/1)^(1*

How To Maximize Your Interest Earnings 

Here are some strategies for maximizing your earnings with both compound and simple interest rates.

Maximizing Earnings with Simple Interest

  • Pay More Frequently: Try to make debt payments more frequently than required to reduce the principal balance faster and pay less interest.
  • Negotiate Lower Rates: Whether saving or borrowing, negotiate for the lowest possible interest rate to maximize earnings or minimize interest payments.
  • Lump-Sum Payments: Make lump-sum payments to reduce the principal quickly, which will reduce the total interest paid over the life of the loan.

Maximizing Earnings with Compound Interest

  • Start Early: The sooner you start saving or investing, the more time your money has to benefit from compound interest.
  • Reinvest Earnings: Reinvest dividends and interest payments to take full advantage of compounding.
  • Increase Compounding Frequency: Choose investments with more frequent compounding periods (e.g., monthly over annually) to compound earnings more often.
  • Regular Contributions: Consistently add to your savings or investment to increase the principal balance, which in turn increases the compound interest earned over time.

Simple or Compound Interest: Which Is Better?

Ultimately, the choice between compound and simple interest will depend on the specific financial product and the institution offering it. It’s critical to understand which type of interest is being applied to any financial product you are considering and how it will affect your payments or earnings over time.

If you invest or save your money, you should look for a financial account that offers compound interest. Compound interest accrues to both the principal balance and the accumulated interest. A frequent compound schedule can help you earn faster returns on your invested money. 

If you want to apply for quick cash loans and borrow money, look for an option that uses simple interest. There are plenty of low interest online loans for bad credit that do not compound the interest. 

FAQs About Compound and Simple Interest Rates

What’s a significant difference between simple and compound interest when it comes to how quickly interest accrues?

The difference lies in the calculation of interest amassed. With simple interest, the annual interest rate applies only to the principal balance, so interest does not compound. Compound interest, however, involves paying interest on both the principal and the interest from previous periods, which can accumulate more rapidly.

Can you give me a simple interest example and how it compares vs compound interest over time?

Sure! For a simple interest example, if you borrow $1,000 at an annual rate of 5%, after one year, you’ll owe $1,050. This amount doesn’t change over time—it’s always 5% of the original $1,000. Vs compound interest, if that same $1,000 compounded annually at the same rate, after one year, you’d owe $1,050, but after two years, you’d owe $1,102.50 because the second year’s interest would also include the first year’s interest.

How does the number of compounding periods affect the amount of interest I’ll pay on a loan?

The number of compounding periods has a direct impact on the amount of interest you’ll pay when borrowing money. The more frequently interest is compounded, the more interest will accrue. For example, if interest is compounded monthly rather than annually, you’ll end up paying interest on the interest accrued each month, which increases the total amount you pay back.

In what scenarios would paying interest with simple interest be more beneficial than using compound interest?

Paying interest with simple interest is generally more beneficial when borrowing money, as it results in lower overall payments. Since simple interest is calculated only on the principal balance, you won’t be charged additional interest on the interest that has already accrued, unlike with compound interest.

What’s a significant difference in the outcome of simple vs compound interest on investments?

The difference is that compound interest can significantly increase the amount of interest earned on investments over time because it takes into account the interest accrued in previous periods. In contrast, simple interest only earns interest on the principal balance, which may result in less interest over the same period.

Is there a simple way to understand how the frequency of compounding affects compound interest?

Absolutely! Think of the frequency of compounding as how often your interest earnings get a boost. With more frequent compounding periods, such as monthly vs annually, your interest is calculated on an increasingly larger balance due to the previous periods’ interest being added to the principal. This means you’re essentially earning “interest on interest” more often.

What factors should I consider when deciding between a loan with simple interest vs compound interest?

When deciding between simple and compound interest loans, consider the total cost of interest payments over the life of the loan. Simple interest tends to be less costly over time. However, compound interest could be more beneficial if you plan to pay off the loan quickly, as the compounding effect won’t have as much time to add to the total cost.

Where can I find a reliable calculator for both simple and compound interest to manage my finances better?

Many financial institutions and educational websites offer online calculators for both simple and compound interest. These tools can help you understand potential interest payments or earnings by inputting your principal balance, the annual interest rate, and the number of compounding periods.

CreditNinja: A Final Note About Interest Rates  

Understanding interest rates and how they work can help you make a well-informed financial decision and better manage your finances. Simple interest keeps calculations clear and predictable for loans, while a compound rate can boost your savings by earning interest on interest over time. 

Check out the CreditNinja Dojo for more educational articles on various financial topics. Learn the pros and cons of a savings account, how to get approved for a personal loan, and even how to get free stuff from the government!

References:

  1. National Rates and Rate Caps │ FDIC
  2. Debt consolidation could save you thousands of dollars │ CBS News
  3. What Is Simple Interest? │ Master Class
  4. Understanding Compound Interest │ Business Insider
  5. The Life-Changing Magic Of Compound Interest │ Forbes

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