**How Does Compound Interest Work?**

Savings compound interest is calculated by taking into account both the initial principal and accumulated interest from previous periods.

“Compound interest,” which is calculated only on the principal amount, is thought to have originated in 17th-century Italy.

When money is compounded, it multiplies at an accelerated rate, and the longer the compounding period, the greater the compound interest.

**KEY TAKEAWAYS**

- In compound interest, the interest on the initial principal of a loan is calculated, as well as all the interest that has accrued from the previous period.
- The power of compound interest comes from generating “interest on interest.”.
- From continuous to daily to annual compounding, interest can be compounded at any time.
- Money multiplies accelerated by compounding.

**Comprehending compound interest**

**The Compound Interest Formula**

In order to calculate compound interest, multiply the initial principal amount by one plus the annual interest rate raised to the number of compound periods minus one.

The following formula can be used to calculate compound interest:

- The compound interest rate is calculated by subtracting the present value of the principal and interest from the future value of the principal and interest.

*= [P (1 + i)**n**] – P*

*= P [(1 + i)**n **– 1]*

Where:

*P = principal*

*i = percentage interest rate on nominal annual loans*

*n = Periods between compounding*

For a $10,000 loan with an interest rate of 5% compounded annually, the interest would be as follows:

*$10,000 [(1 + 0.05)**3** – 1] = $10,000 [1.157625 – 1] = $1,576.25*

**Interest compounded over a period of time**

A compound interest rate grows at an ever-accelerating rate because it incorporates interest from previous periods. In the example above, though the total interest payable over the three years of this loan is $1,576.25, the interest amount is not the same for all three years, as would be the case with simple interest. Below you will find the interest due at the end of each year.

Long-term investment returns can be greatly boosted by compound interest. A $100,000 deposit earning 5% simple interest over a 10-year period would earn $50,000 in interest, but a $10,000 deposit earning 5% compound interest would earn $62,889.46. The total interest would rise to $64,700.95 if the compounding period were instead paid monthly over the same 10-year period at 5% compound interest.

**Interest schedules for compound interest**

Financial instruments usually use standard compounding frequency schedules. Interest can be compounded on any given frequency schedule, from daily to annual.

For savings accounts, compounding occurs daily, monthly, or semiannually; for certificates of deposit (CDs), compounding occurs daily, monthly, or semiannually; and for money market accounts, it is usually daily. The most common compounding schedule for home mortgages, home equity loans, personal business loans, or credit card accounts is monthly.

It is also possible for accrued interest to be credited to the existing balance in a different time frame. Interest may compound on an account daily, but only be credited monthly. The interest will only begin to earn additional interest in the account when it is credited, or added to the existing balance.

It is also possible to get continuously compounding interest from some banks, which adds interest to principal every time it can be paid. If you don’t want to put money in and take it out on the same day, it doesn’t accrue that much more interest than daily compounding interest.

Investors or creditors benefit from compounding interest more frequently. Borrowers, however, do not.

**Periods of compounding**

It is important to understand that the number of compounding periods makes a significant difference in compound interest calculations. The basic rule is that the more compounding periods, the greater the compound interest amount.

An annual 10% interest rate on a $10,000 loan over a period of ten years can result in a significant difference in the number of compounding periods.

**Saving early is the key to compound interest**

For people in their 20s, retirement is often neglected because it seems so far away that other expenses seem more important. Compound interest comes in handy at a time when saving small amounts can pay off massively later in life—far more than saving higher amounts. As an example, here’s what it looks like.

Suppose you invest $100 a month in the market when you are in your 20s. Suppose you average 1% positive returns each month (12% annual), compounded monthly over the next 40 years. You start investing at the same age, but your twin does not begin investing until 30 years later. Investing $1,000 a month for 10 years, your tardy sibling averages a positive return of 5%.

After 40 years, your twin will have saved about $230,000, whereas you will have about $1.17 million when you hit the 40-year mark and his twin has saved for 10 years. The miracle of compound interest makes your portfolio significantly larger, here by a factor of a little more than five, even though your twin invested ten times more than you did (and even more toward the end).

Opening an individual retirement account (IRA) or taking advantage of a retirement plan offered by your employer, such as a 401(k) or 403(b), is a smart decision. You’ll be glad you did.