What Is Compound Interest?

Compound interest is interest that's calculated on both the initial principal of a deposit or loan and on all accumulated interest. It's a tremendous advantage for savers and investors but not so much for borrowers.

Savers and investors benefit from the powerful growth in the value of their financial accounts that compounding interest provides over time. Compounding interest and growth in balance means that b🔥orr𓆏owers have to pay more to get out of debt.

How Compound Interest Works

澳洲幸运5官方开奖结果体彩网:Compound interest is calculated on the 澳洲幸运5官方开奖结果体彩网:principal or initial deposit in your account and ꧙on the interest that money earns. Subsequen🍸t compound interest calculations apply to larger amounts as interest increases your account's value,

Compound interest works in your favor

Let's say you have an account with a deposit of $100 that earns a 10% annual compounded interest rate. That $100 grows to $110 after the first year:

$100 x .10 = $10

$100 + $10 = $110 new balance

The account valওue thꦕen grows to $121 when interest is calculated after the second year. 

$110 x .10 = $11

$110 + $11 = $121 new balance

The second year's gain is $11 instead of $10 because the 10% rate was applied to a larger account balance. The 10% interest applied to $100 created a new balance of $110. The 10% was applied to that new balance of $110 after year two for a third new balance of $121. The 10% will be applied to $121 and a larger new balance will be the result at the end of the third year.

Compound interest can work against you

Now let's say that you borrowed $100 at a compound interest rate of 10% that's applied annually. You'll have $100 in principal and $10 in interest after one year using the same calculation for a total amount owed by you of $110. 

澳洲幸运5官方开奖结果体彩网: $100 x .10 = $10

$100 + $10 = $110 new balance

The 10% interest rate is applied to both the principal of $100, r꧒esulting in $10 of interest, and the accumulated interest of $10, resulting in $1 of interest in year two. This results in a total of $11 in interest gained that year which is $21 foꦇr both years: $10 after year one plus $11 after year two.

澳洲幸运5官方开奖结果体彩网: $100 x .10 = $10

澳洲幸运5官方开奖结果体彩网: $10 x .10 = $1

$10 + $1 = $11 total new interest

$110 + $11 = $121 new balance 

Compound interest is working against you by increasing the amount you must pay back to the lender so you'll want to pay off your debt as soon as possible.

Formula for Compound Interest

The compound interest formula is similar to the Compound Annual Growth Rate (CAGR). You're computing a rate that links the return over several periods for CAGR. You most likely know the rate already for compound interest and are just calculating what the future value of the return might be. 

Just algebraically rearrange the 💮foꦆrmula for CAGR to find the formula for compound interest. You'll need:

• The beginning value
• The interest rate
• The number of periods in years

The interest rate and number of periods must be expressed in annual terms because the length is presumed to be in years. You can solve for the future value from there💟:

$\begin{aligned}&\text{Beginning Value}\\&\times\left(1+\left(\frac{\text{interest rate}}{\text{NCPPY}}\right)\right)^{(\text{years}\ \times\ \text{NCPPY)}\ =\ \text{Future Value}}\\&\textbf{where:}\\&NCPPY=\text{number of compounding periods per year}\end{aligned}$​Beginning Value×(1+(NCPPYinterest rate​))(years × NCPPY) = Future Valuewhere:NCPPY=number of compoundi🗹ng periods per🦩 year​

This formula looks more complex than it is because of the requirement to express it in💙 annual terms. 

Keep in mind that the number of compouꦫnding periods per year is one if it's an annual rate. This means you're dividing the interest rate by one and multiplying the years by one. You would divide the rate by four and multiply𝄹 the years by four if compounding occurs quarterly.

Calculating Compound Interest in Excel

The best practices of financial modeling require that calculations be transparent and easily auditable. The problem with piling all the calculations into a formula is that you can't easily see what numbers go where. You can't easily tell which numbers are user inputs and which are hard-coded. 

🤡You can set up the calculation in Excel in three 🦩ways to avoid these problems:

1. Including all the data in one table is the easiest to audit and understand.
2. You can also break out the calculations line by line.
3. Another option is to calculate the whole equation in one cell to arrive at just the final value figure.

Examples of these♑ methods are shown here in order:

The Bottom Line

Excel can be a helpful and powerful partner when you want to calculate compound interest amounts for different purposes such as loans and investments. It's especially convenient when frequent intervals are involved over multiple years and accuracy counts.