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Interest & APR

Calculator Use

The compound interest calculator finds total account value, principal plus compound interest accrued over time. The answer shows the steps to calculate compound interest, and creates a bar chart to show how your investment grows with interest compounding -- when you earn interest on interest.

You can calculate compound interest on a 401K, savings account or any investment that accrues interest. The calculator uses the compound interest formula A=P(1 + r/n)^nt where A is total principal plus accrued interest, P is the starting principal, r is the interest rate as a decimal, n is compounding frequency, and t is length of time for the investment.

Why Use a Compound Interest Calculator

See how interest compounding works for CDs, 529 accounts, Roth IRA holdings, retirement accounts or any interest-earning investment. Input any 4 values of principal, interest, rate, time or compounding frequency and calculate the missing value. The compound interest growth chart shows you how interest increases exponentially across the investment holding period.

Experiment by changing the values of your inputs, for example the starting principal or the length of your investment, to see results in the compound interest chart. Noting which values deliver the best result for your investments can inform your future financial goals and plans.

Recent updates to the calculator allow you to enter regular contributions or withdrawals on your investment. Enter these optional values and select frequency and transaction timing.

What is Compound Interest?

Compound interest is when interest you earn on a savings account or investment is rolled back into your balance to earn additional interest. The compound interest calculation accounts for interest you earn over time and adds it back into the amount being invested or saved. So while you are earning interest on your original principal you are also earning interest on the accumulated interest.

Compound interest is different from simple interest, where the interest amount is calculated as a flat percentage of the value of the investment. Simple interest is not rolled back into the balance, and there are no ongoing interest calculations.

The Compound Interest Formula

This calculator uses the compound interest formula to find the total principal plus accrued interest. It uses this same formula to solve for principal, interest, rate or time given the other known values. You can also use the compound interest equation to set up compound interest calculations in Excel¹ or other spreadsheet software.

A = P(1 + r/n)^nt

In the formula:

• A = Final amount (principal + accrued interest)
• P = Principal starting amount
• r = Annual nominal interest rate as a decimal
• R = Annual nominal interest rate as a percent: r = R/100
• n = number of compounding periods per year
• t = time in years

Other variables used in the calculation and solution:

• I = Interest amount
• PMT = Payment, if you are making regular deposits or withdrawals
• q = how many deposits or withdrawals in a year
• ln = natural logarithm, used to "undo" the exponents when calculating for time

Using the Compound Interest Calculator: Example

Say you have an investment account that increased from $30,000 to $33,000 over 30 months. If your local bank offers a savings account with daily compounding (365 times per year), what annual interest rate at the bank matches the rate of return in your investment account?

In the compound interest calculator select "Calculate Rate". The calculator uses the equations: r = n((A/P)^1/nt - 1) and R = r*100.

Enter:

• Total P+I: $33,000
• Principal: $30,000
• Compounding: Daily (365)
• Time: 2.5 years (30 months divided by 12 equals 2.5 years)

Showing the work using the rate formula r = n((A/P)^1/nt - 1)

\[ r = 365 \left(\left(\frac{33,000}{30,000}\right)^\frac{1}{365\times 2.5} - 1 \right) \] \[ r = 365 (1.1^\frac{1}{912.5} - 1) \] \[ r = 365 (1.1^{0.00109589} - 1) \] \[ r = 365 (1.00010445 - 1) \] \[ r = 365 (0.00010445) \] \[ r = 0.03812605 \] \begin{align} R = r \times 100 \\[0.5em] R = 0.03812605 \times 100 \\[0.5em] R = 3.813\% \end{align}

Your result: R = 3.813% per year

So you'd need to put $30,000 into a savings account that pays a rate of 3.813% per year and compounds interest daily in order to get the same return as your investment account.

Compound Interest Formulas for Excel

We provide Excel formulas for compound interest calculations in the tables below. Copy the formulas and paste them in spreadsheet software such as Excel, Google Sheets or Apple Numbers.

To copy these examples correctly, start your mouse outside the table upper left corner. Drag your mouse to the outside of the lower right corner. Be sure all text inside the table is selected. Copy the table onto your clipboard and paste it into cell A1 of your spreadsheet. These formulas will only work if you paste into cell A1 but you can modify them if you need to paste into different rows or columns by editing the "B" reference cells in the formulas.

Calculate Total Principal Plus Interest (Future Value FV) using A = P(1 + r/n)^nt

For this example let's start with a principal investment of $10,000 at a rate of 3% compounded quarterly (4 times a year) for 5 years. If you copy and paste the formula table into cell A1 of your spreadsheet, you should see the answer 11,611.84 in cell B1. You may need to format your cells so they show two decimal places, and dollar signs if you like. Edit the values in cells B2, B3, B4 and B5 for your specific interest calculations.

Total Principal Plus Interest (FV) $	= ROUND(B3 * POWER(( 1 + ((B2/100)/B4)),(B4*B5)),2)
Rate %	3
Principal $	10000
Compounding per year	4
Years	5

 

Calculate Rate using Rate Percentage = n(((A/P)^(1/nt)) - 1) * 100

In this example let's start with a principal of $10,000 with interest of $500. This results in a total principal plus compound interest amount of $10,500 over 2 years compounded monthly (12 times per year). Copy and paste the formula table below into column A1 of your spreadsheet. You should see the answer for Rate % = 2.44 in cell B1. Change the values in cells B2, B3, B4 and B5 for your specific interest rate calculation.

Rate %	= ROUND(B4*((POWER((B2/B3),(1/(B4*B5))))-1)*100,2)
Accrued Amount $	10500
Principal $	10000
Compounding per year	12
Years	2

 

Additional Resources

We have moved our extensive list of compound interest calculation formulas and derivations to their own Compound Interest Calculator Resources page. Consult this page to find formulas rearranged to solve for any given variable in the compound interest calculation.

Visit InterestMagician.com for interactive compound interest calculations. There, you can experiment with investment values, interest rates and lengths of deposit and visualize your earnings over time.

Visit the CalculatorSoup® Simple Interest Calculator to read more about simple interest. Learn that without exponents, interest calculations using the simple interest formula A = P(1 + rt) are very different from compound interest calculations.

Notes

¹Excel is a registered trademark of Microsoft Corporation.