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Compound interest is the interest you earn on both your initial savings deposit and the interest already accrued and credited to your savings balance. It’s an easy way to build savings because each interest payment results in returns on your initial deposit, even if you never deposit more funds. This snowball effect is often referred to as “the miracle of compound interest.”
Here’s how compound interest works, how to calculate it, and how to maximize your savings:
What is compound interest?
When you have a bank or investment account that earns interest, the financial institution compounds your accumulated interest and credits it to your account on a regular basis. Because the calculation is compounded — that is, calculated based on the entire balance, including interest previously credited to your account — the rate of growth increases as your balance grows.
How does compound interest work?
The following example will help you understand exactly how compound interest works. Say you deposit $1,000 into a high-yield savings account with a simple interest rate of 5% (which is much higher than you’ll find with a standard savings account).
- Year 2: 5% interest on $1,050 equals $52.50, bringing your balance to $1,102.50
- Year 3: 5% interest on $1,102.50 equals $55.13 (rounded), bringing your balance to $1,157.63
- Year 4: 5% interest on $1,157.63 equals $57.88, bringing your balance to $1,215.51
- Year 5: 5% interest on $1,215.51 equals $60.78 (rounded), bringing your balance to $1,276.29
Had the bank only paid interest on the initial $1,000, the account would have earned just $50 per year, or $250 after five years. Instead, it earned $276.29.
What is the formula for calculating compound interest?
The formula for calculating compound interest can be expressed in a couple different ways, but this a common one:
Each letter in the compound interest formula represents a value:
- A: The total amount you’ll have at the end of the period for which you’re calculating compound interest
- P: The principal amount, which is your initial investment
- R: The annual interest rate, expressed as a decimal
- N: The number of times the interest compounds each year
- T: The amount of time the interest accumulates
The formula is less complicated than it looks. You simply use values you know to figure out the values you don’t know.
If, for example, you want to compare savings accounts and know how much you’ll deposit and how long you’ll keep the money in savings, you have the values for (P) and (t) right off the bat. As you research accounts, you find the interest rate (r) and compounding frequency (n) for each. You now have all the information you need to figure out A, the total you’ll have at the end of the time period, for each account you’re considering.
The following table illustrates how time and frequency affect the total. It assumes a $1,000 initial deposit and an annual interest rate of 5%.
|Compounds daily||Compounds monthly||Compounds annually|
|After one year||$1,051.27||$1,051.16||$1,050|
|After two years||$1,105.16||$1,104.94||$1,102.50|
|After five years||$1,284||$1,283.36||$1,276.28|
|After ten years||$1,648.66||$1,647.01||$1,628.89|
Note that compound interest has the same effect on debts you’re paying interest on, such as credit card debt. The higher the rate and the more frequently interest is compounded, the faster your debt grows.
Taking advantage of compound interest when opening a savings account
Compound interest is like free money that makes your savings grow. Here are some tips for maximizing your earnings:
- Start saving early. The sooner you save, the more time your interest has to compound.
- Check the frequency of compounding. Frequent compounding, such as daily or monthly, results in more earnings than annual compounding does.
- Find the highest APY. The annual percentage yield is the total interest you’ll earn over the course of a year. The calculation includes both the percentage rate and the frequency of compounding, so it’s a more accurate metric than the annual interest rate alone.
Compound interest and debt
Compound interest can have a major effect on debt. Daily compounding, which is typical for credit cards, magnifies the effect and extends the time it takes for you to get out of debt if you only make minimum payments.
For example, say you have a $1,000 credit card balance with a 15% APR. If you make minimum payments of $25 per month, it would take 56 months to pay off the debt and you’d pay a total of $394.98 in interest — almost 40% of the original debt.
When the interest rate on debt is so high that minimum payments don’t keep up with the interest charges — a situation referred to as negative amortization — you could find yourself going deeper into debt even if you never miss a payment.
A personal loan can be an excellent solution for consolidating compounding and high-interest debt. Personal loans have fixed rates that are often lower than credit cards and payday loans, so you can save on interest and get out of debt sooner.