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Loan Basics

How Does Compound Interest Work?

Compound interest occurs when interest gets added to the principal amount invested or borrowed, and then the interest rate applies to the new (larger) principal. It's essentially interest on interest, which over time leads to exponential growth.

Compounding can work to your advantage as your savings and investments grow over time—or against you if you're paying off debt. Read on for more about how compound interest works and how it can affect your finances.

How Does Compound Interest Work?

Say you put $1,000 into a savings account with a 10% interest rate (an unrealistically high rate, but helpful for examples) that compounds annually. At the end of the first year, you'll have $1,100—the initial $1,000 in principal plus $100 in interest. That $100 is "simple" interest—interest based only on the principal amount invested.

At the end of the second year, you'll have $1,210—the $1,100 from the previous year plus $110 in added interest (10% of $1,100). Instead of calculating interest based only on your original principal, compounding interest calculates your annual interest based on the principal plus any previous interest you earned on that principal.

By the end of the 10th year, you'll have $2,594, more than double your initial savings (without adding any more of your own money after your initial investment). You can thank compound interest for that.

What Is the Formula for Compound Interest?

The compound interest formula is:

A = P(1+r/n)nt

  • P is the principal (the starting amount)
  • r is the annual interest rate, which is written as a decimal
  • n is the number of times the interest compounds each year
  • t is the time, or total number of years
  • A is the total amount you will wind up with at the end of the timeframe

Fortunately, you don't need to be a math whiz to put the formula to work. You can use one of the many online calculators to figure out how much interest will accrue and how compounding can impact your savings or debt. However, the formula can offer insight into how compounding works.

Whether you're saving or borrowing money, you may already know the amount you'll start with (P) and your timeframe (t). As a result, there are two variables to consider as you compare your options—the interest rate (r) and compounding frequency (n).

The impact of a higher or lower interest rate is fairly straightforward. A higher rate means more interest gets added each cycle.

Similarly, the more often interest compounds, the faster the growth. For example, here's how different frequencies impact the growth of $1,000 with a 10% interest rate.

Compounds dailyCompounds monthlyCompounds annually
After one year$1,105$1,105$1,100
After two years$1,221$1,220$1,210
After five years$1,649$1,645$1,611
After 10 years$2,718$2,707$2,594

How Does Compound Interest Affect Debt?

While compound interest can help your savings grow more quickly than it would with simple interest, it can also work against you when you're borrowing money.

Many credit cards compound interest daily on average daily balances. While the calculation is complicated, the bottom line isn't: Compound interest on credit cards adds to your debt when you carry over a balance from month to month. The (often high) interest rate and daily compounding are two reasons paying off credit card debt can be difficult—and why you should always try to pay your credit card balance in full each month. That way you're charged zero interest and don't have to worry about compounding interest on your debt at all.

Some types of loans, such as federal student loans and mortgages, generally don't have daily compounding interest. As long as your monthly payment covers the accrued interest, then the interest doesn't compound.

However, if your monthly payment doesn't cover the monthly interest, then your overall loan balance may grow—what's known as negative amortization. If the unpaid interest gets added to your principal balance, then the interest rate may apply to that larger balance (in other words, the interest compounds).

When you're applying for any type of loan, but especially a large loan, make sure you understand how interest accumulates and when it compounds (if at all).

Using Your Knowledge of Compounding Interest

You can make more strategic financial decisions once you understand how compounding works. For example, look for a savings account that offers daily (rather than monthly or yearly) compounding and transfer your savings into the account as frequently as possible. On the flip side, make credit card payments throughout the month to decrease how much interest accrues and compounds—and pay off your balance in full each month whenever possible.

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