With simple interest, you earn a rate of interest annually without interest earned being added to the principal. Compound interest allows earned interest to be added to the principal. Going forward, interest is paid on that new amount. Compound interest is calculated based on the principal amount (the initial size of the deposit) as well as the interest it accumulates over time. Interest can compound at different rates (for example, daily, monthly or quarterly).
Savings products like traditional savings accounts, money market accounts, CDs, and savings and CDs in retirement accounts all typically compound interest.
Formula for compound interest
The compound interest formula considers:
- Your principal
- Interest rate
- Time and compounding frequency, which are typically daily, monthly or annually
The formula below will tell you how much interest you'll earn over that period.
The compound interest formula is:
Initial principal amount multiplied by (1 plus the annual interest rate, divided by the number of compounding periods in a year, raised to the number of compounding periods multiplied by time)
OR
A = P (1 + r/n) (nt)
P is your principal (initial deposit)
r is the annual rate of interest as a decimal
t is the length of time the principal is on deposit
n is the number of times interest is compounded per unit of t
A is the future value you will have at the end of the time period
You can use the formula to explore different scenarios and see how compound interest can make a real difference in your savings and life goals.
Compound interest formula in action: daily, monthly and yearly compounding
Example of interest compounding annually
Let's see examples of how the compounding interest formula works using a hypothetical rate.
Say you deposit $10,000 in a savings account that earns a 2.3%* annual rate of return. Use the compound interest formula to calculate the amount you would have at the end of a savings period for different compounding options.
A = P (1 + r/n) (nt)
Starting with a balance of $10,000 and a 2.3%* annual rate of return, after one year you can end up with as much as $10,233 in a savings account.
| Formula | Compounding Yearly | Compounding Monthly | Compounding Daily |
|---|---|---|---|
| Principal P | $10,000 | $10,000 | $10,000 |
| Rate r | .023* | .023* | .023* |
| Time t | 1 | 1 | 1 |
| Periods n | 1 | 12 | 365 |
| Future Value A | $10,230 | $10,232 | $10,233 |
Notice how the more frequently your interest is compounded, the more interest you earn.
What could happen if you save that $10,000 for 5 years instead? That initial deposit can grow via compounding by more than $1,200 with a 2.3%* annual rate.
| Formula | Compounding Yearly | Compounding Monthly | Compounding Daily |
|---|---|---|---|
| Principal P | $10,000 | $10,000 | $10,000 |
| Rate r | .023* | .023* | .023* |
| Time t | 5 | 5 | 5 |
| Periods n | 1 | 12 | 365 |
| Future Value A | $11,204 | $11,217 | $11,219 |
If you really want to reap the advantages of compound interest, consider the potential impact of regular contributions. For example, by contributing $100 per month to your savings, it may grow to as much as $17,565 after 5 years at a 2.3%* annual rate of return.
| Formula | Compounding Yearly | Compounding Monthly | Compounding Daily |
|---|---|---|---|
| Principal P | $10,000 | $10,000 | $10,000 |
| Rate r | .023* | .023* | .023* |
| Time t | 5 | 5 | 5 |
| Periods n | 1 | 12 | 365 |
| Monthly Deposit | $100 | $100 | $100 |
| Future Value A | $17,565 | $17,582 | $17,583 |
Remember, you started with a balance of simply $10,000.
What you should know about compound interest and your savings accounts
When you open or add money to a savings account, read the rate sheet or account disclosures to determine how frequently interest compounds for your account. You can use a compound interest calculator to estimate how much interest you could earn.
*Rate provided is for illustrative purposes only.
