Month | Date | Payment | Principal + Payments | Interest | Cumulative Interest | Balance |
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# Compound Daily Interest Formula

The concept of compound interest has fascinated financial experts and investors for centuries. That’s because the apparently simple mathematics involved in the compound interest formula brings surprising results. Putting even a small amount of money into an interest-bearing account and leaving it there for years can cause the initially tiny sum to grow significantly.

The best way to get a grasp of the concept is to break down the compound interest formula into its component parts and look at an example scenario of a long-term investment. Equally helpful is understanding how a reverse compound interest calculator works, as well as a continuous compound interest calculator. For anyone interested in working with a compound interest calculator, Excel is a useful program to understand.

Keep in mind that most banks and other kinds of financial institutions pay interest in periods. Years, quarters, months, days, and “continuous” periods are the most common methods for building up interest on a principal amount of deposit.

Here are the core concepts behind using a continuous compound interest calculator and a reverse compound interest calculator, or one that uses any period to figure the total accumulated amount of interest at a given point in the account’s life.

### Pieces of the Puzzle

When it comes to using a compound interest calculator, Excel spreadsheets are your friend. They can prompt you to fill in all the blanks and come up with a final total. For example, a compound interest calculator shows that a daily compounding method is a faster way to grow your balance than quarterly or annual interest payments.

The least you need to know to build the formula are the following values:

- The number of time periods that have passed: T
- The frequency with which interest is paid during each period: N
- The interest rate: R
- The initial balance, or principal: P

When using a compound interest calculator, quarterly payments are a common frequency to use for many types of accounts. However, in the example below, annual payments will be used for the sake of simplicity.

### The Formula

This is the formula to calculate the total amount of money after a certain amount of time:

Final Amount = P * (1 + R/N) ^ (N * T)

More frequent interest payments, as is the case with compound interest calculator daily frequencies, will bring in some complex calculations. But there is no need to worry, as an Excel spreadsheet will handle all the calculations for you. For the sake of brevity and ease of understanding, it is important to begin with a simple scenario.

### A Simple Example

In the following example, suppose you put $1,000 into a 5 percent interest-bearing account, which pays annually, and leave it there for 40 years, as a 25-year-old might do with a retirement savings arrangement. The important values are annual interest payments (N = 1), a principal of $1,000 (P = $1,000), an interest rate of 5 percent (R = .05), and 40 time periods (T = 40). Remember, you are apt to encounter quarterly compound interest payments, so adjust the frequencies accordingly in the compound interest formula for those scenarios.

Here’s what you’d have after the 40 years elapsed:

Final amount = P * (1 + R/N) ^ (N * T)

= $1,000 * (1 + .05/1) ^ (1 * 40)

= $1,000 * (1.05) ^ (40)

= $1,000 * 7.04

= $7,040

Your initial investment of $1,000 will grow to more than eight times its original size during the 40-year period, assuming a 5 percent annual interest rate and no withdrawals from the account.