According to Albert Einstein, compound interest is the “eighth wonder of the world. He who understands it earns it…he who doesn’t… pays it.”
While some say Einstein also called compound interest the most powerful force in the universe, it is undoubtedly one of the most powerful financial forces on earth. Understanding how compound interest works is the key to long-term financial success.
Whether you are borrowing money for student loans, purchasing a home, or investing your savings, the power of compounding has a huge effect on your money.
What’s the compound interest formula?
We all know interest is simply a percentage of funds paid to a borrower or lender.
For instance, if you deposit $1,000 into a one-year certificate of deposit account that’s paying 5.00% interest, you will get $50 back plus the original $1,000.
But what happens if you take that $1,050 and deposit it again with the same 5.00% interest rate? You earn $52.50 thanks to a higher deposit amount, leaving you with a grand total of $1102.50. And if you deposit your full $1102.50, you end up with $1157.63, and so on.
That’s compounding interest. You can continue to earn, or pay, interest on prior interest after each compounding period. In the example above, the 5.00% interest compounded annually. But in most cases, you will find that interest compounds monthly.
That’s where the compound interest formula comes in.
A = P (1 + r/n) ^ nt
A = the future value of the investment/loan, including interest
P = the principal investment amount (the initial deposit or loan amount)
r = the annual interest rate (decimal)
n = the number of times that interest is compounded per year
t = the number of years the money is invested or borrowed for
The power of compound interest
The compound interest formula is not easy for everyone to follow, so let’s take a look at another example.
This time, we will look at someone saving in a retirement account. Let’s say a 22-year old recent college graduate earns $40,000 per year and is saving 10% of their salary, or $4,000 per year.
In this case, our saver is putting in $333.33 per month and earning a 6% return, compounded monthly.
At the end of year one, this person would have contributed $4,000, but has $4,132.37 saved thanks to monthly compounding. After another year, the ending balance is $8,519.69. In just two years this person has over $500 in compounded interest earnings!
But saving for retirement is not a one or two year process. It takes place over decades. That’s the secret sauce of the compound interest formula.
In 10 years, this person’s balance is $14,899. After 20 years, it’s $154,782, of which nearly $75,000 came from interest. At 30 years the balance is $336,509, of which over $200,000 comes from interest. And in 40 years when this person is 62 years old, the balance is $667,143, of which $507,000 came from interest.
When you think about it, that is spectacular. Putting away $160,000 over 40 years, you end up with $667,000. That is a huge return on investment. All it takes is a significant amount of time for the compound interest formula to really make an impact.
“That’s what’s so frustrating,” says Retirement Answer Man Rodger Whitney. “It takes years of compounding before it becomes life changing. It will, though, if you’re patient.”
That’s why starting young and contributing regularly to a retirement account is so important.
Compound interest and student loans
Interest compounding not only occurs with bank accounts, it happens on loans as well. It just works a little differently.
Interest compounds the same way with a principal balance. However, since borrowers make regular payments, the principle goes down each month. Simultaneously, the accrued interest goes down as well.
The process of calculating compound interest on a loan with a fixed payment each period is called amortization. Using amortization tables or calculators, you can see how much interest is paid over the life of the loan, assuming only the minimum loan payments are paid.
However, if you’re interested in seeing how much money you can save by making extra monthly payments on a student loan, check out the Student Loan Hero payoff calculator below.
Use this knowledge to get out of debt and save
Just as compound interest on savings and investments can make you rich, knowing how the compound interest formula works with loans can save you thousands of dollars. The power of interest is one of the most important forces in your finances, and shouldn’t be taken lightly.
Don’t sit back and let compound interest determine your financial fate. Take control and use compound interest to your advantage. It can completely change your financial future in a positive way.
Pay off your debt, save aggressively, and watch your net worth begin to climb. That’s harnessing the power of compound interest.
Interested in refinancing student loans?Here are the top 6 lenders of 2018!
|Lender||Variable APR||Eligible Degrees|
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1 Important Disclosures for Earnest.
To qualify, you must be a U.S. citizen or possess a 10-year (non-conditional) Permanent Resident Card, reside in a state Earnest lends in, and satisfy our minimum eligibility criteria. You may find more information on loan eligibility here: https://www.earnest.com/eligibility. Not all applicants will be approved for a loan, and not all applicants will qualify for the lowest rate. Approval and interest rate depend on the review of a complete application.
Earnest fixed rate loan rates range from 3.89% APR (with Auto Pay) to 5.87% APR (with Auto Pay). Variable rate loan rates range from 2.47% APR (with Auto Pay) to 5.87% APR (with Auto Pay). For variable rate loans, although the interest rate will vary after you are approved, the interest rate will never exceed 8.95% for loan terms 10 years or less. For loan terms of 10 years to 15 years, the interest rate will never exceed 9.95%. For loan terms over 15 years, the interest rate will never exceed 11.95% (the maximum rates for these loans). Earnest variable interest rate loans are based on a publicly available index, the one month London Interbank Offered Rate (LIBOR). Your rate will be calculated each month by adding a margin between 1.82% and 5.50% to the one month LIBOR. The rate will not increase more than once per month. Earnest rate ranges are current as of Month/Day/Year, and are subject to change based on market conditions and borrower eligibility.
Auto Pay discount: If you make monthly principal and interest payments by an automatic, monthly deduction from a savings or checking account, your rate will be reduced by one quarter of one percent (0.25%) for so long as you continue to make automatic, electronic monthly payments. This benefit is suspended during periods of deferment and forbearance.
The information provided on this page is updated as of 08/21/18. Earnest reserves the right to change, pause, or terminate product offerings at any time without notice. Earnest loans are originated by Earnest Operations LLC. California Finance Lender License 6054788. NMLS # 1204917. Earnest Operations LLC is located at 302 2nd Street, Suite 401N, San Francisco, CA 94107. Terms and Conditions apply. Visit https://www.earnest.com/terms-of-service, email us at email@example.com, or call 888-601-2801 for more information on ourstudent loan refinance product.
© 2018 Earnest LLC. All rights reserved. Earnest LLC and its subsidiaries, including Earnest Operations LLC, are not sponsored by or agencies of the United States of America.
2 Important Disclosures for Laurel Road.
Laurel Road Disclosures
Savings example: average savings calculated based on single loans refinanced from 9/2013 to 12/2017 where borrowers’ previous rates were disclosed. Assumes same loan terms for previous and refinanced loans, and payments made to maturity with no prepayments. Actual savings for individual loans vary based on loan balance, interest rates, and other factors.
Application detail: 5 minutes indicates typical time it takes to complete application with applicant information readily available. It does not include time taken to provide underwriting decision or funding of the loan.
Instant rates mean a delivery of personalized rates for those individuals who provide sufficient information to return a rate. For instant rates a soft credit pull will be conducted, which will not affect your credit score. To proceed with an application, a hard credit pull will be required, which may affect your credit score.
Total savings calculated by aggregating individual average savings across total borrower population from 9/2013 to 12/2017. Individual average savings calculation based on single loans refinanced from 9/2013 to 12/2017 where borrowers’ previous rates were provided. Assumes same loan terms for previous and refinanced loans, and payments made to maturity with no prepayments. Actual savings for individual loans vary based on loan balance, interest rates, and other factors.
3 Important Disclosures for SoFi.
4 Important Disclosures for LendKey.
Refinancing via LendKey.com is only available for applicants with qualified private education loans from an eligible institution. Loans that were used for exam preparation classes, including, but not limited to, loans for LSAT, MCAT, GMAT, and GRE preparation, are not eligible for refinancing with a lender via LendKey.com. If you currently have any of these exam preparation loans, you should not include them in an application to refinance your student loans on this website. Applicants must be either U.S. citizens or Permanent Residents in an eligible state to qualify for a loan. Certain membership requirements (including the opening of a share account and any applicable association fees in connection with membership) may apply in the event that an applicant wishes to accept a loan offer from a credit union lender. Lenders participating on LendKey.com reserve the right to modify or discontinue the products, terms, and benefits offered on this website at any time without notice. LendKey Technologies, Inc. is not affiliated with, nor does it endorse, any educational institution.
5 Important Disclosures for CommonBond.
6 Important Disclosures for Citizens Bank.
Citizens Bank Disclosures
|2.47% – 6.99%3||Undergrad & Graduate|
|2.47% – 5.87%1||Undergrad & Graduate|
|2.47% – 8.03%4||Undergrad & Graduate|
|2.95% – 6.37%2||Undergrad & Graduate|
|2.48% – 6.25%5||Undergrad & Graduate|
|2.72% – 8.32%6||Undergrad & Graduate|