Here’s How the Compound Interest Formula Works

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.

Student Loan Prepayment Calculator

  • Monthly Payment

  • Interest Paid

  • Total Amount Paid

  • Time to Repayment

OriginalPrepaymentSavings
Monthly Payment
Interest Paid
Total Amount Paid
Time to Repayment

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.

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