Compound Interest Calculator: Savings Growth & Monthly Deposits

How compound interest builds wealth over time

Compound interest occurs when earnings generated on your principal investment begin generating their own earnings. Rather than earning simple interest purely on your original deposit, compounding creates exponential growth as accumulated returns are repeatedly reinvested into the principal base.

This calculator lets you simulate initial lump-sum deposits alongside recurring monthly contributions across multiple compounding frequencies. Calculations run entirely in your local browser, keeping your savings and balance figures private.

The compound interest formula with monthly contributions

$$\text{Total Future Balance } A = P \left(1 + \frac{r}{n}\right)^{nt} + PMT \times \frac{\left(1 + \frac{r}{n}\right)^{nt} - 1}{\frac{r}{n}}$$

Variable definitions:

• $P$ (Initial Principal): Starting deposit balance at day zero.
• $PMT$ (Regular Monthly Contribution): Additional cash added at the end of each payment period.
• $r$ (Annual Nominal Interest Rate): Annual rate expressed as a decimal (e.g., 7% = 0.07).
• $n$ (Compounding Frequency per Year): Number of compounding cycles per year (12 for monthly, 4 for quarterly, 1 for annual, 365 for daily).
• $t$ (Duration in Years): Total investment horizon.
• $nt$ (Total Compounding Periods): The cumulative number of compounding cycles over the investment lifetime.

Worked example: $10,000 deposit + $500 monthly contributions

Let us evaluate a 10-year investment plan in a diversified index fund yielding an estimated 7.0% annual return compounded monthly:

• Initial Deposit ($P$): $10,000
• Monthly Contribution ($PMT$): $500
• Annual Interest Rate ($r$): 7.0% ($0.07$)
• Compounding Cycles ($n$): 12 times per year
• Duration ($t$): 10 years ($120$ months)

Step-by-step arithmetic:

1. Periodic Rate ($\frac{r}{n}$): $\frac{0.07}{12} \approx 0.0058333$ per month
2. Growth Factor $(1 + \frac{r}{n})^{nt}$: $(1.0058333)^{120} \approx 2.00966$
3. Growth on Initial Principal: $$10,000 \times 2.00966 = \mathbf{$20,096.61}$
4. Growth on Monthly Contributions: $$500 \times \frac{2.00966 - 1}{0.0058333} = \mathbf{$86,542.40}$
5. Total Future Portfolio Balance: $$20,096.61 + $86,542.40 = \mathbf{$106,639.01}$
6. Total Out-of-Pocket Deposits: $$10,000 + ($500 \times 120) = \mathbf{$70,000.00}$
7. Pure Compound Interest Earned: $$106,639.01 - $70,000.00 = \mathbf{$36,639.01}$

By systematically adding $500 each month, your actual cash contributions of $70,000 yielded $36,639.01 in passive compounded growth, representing over 34% of your total final wealth.

How compounding frequency changes your return

To understand the mathematical effect of compounding frequency, compare the final balance of a $10,000 deposit earning 7% annual interest over 10 years (with zero additional contributions):

More frequent compounding increases returns because accrued interest is credited to the principal base faster, generating a slightly higher Effective Annual Rate (EAR).

Frequently asked questions

What is the Rule of 72?

The Rule of 72 is a quick mental math shortcut to estimate how many years it takes for an investment to double. Divide 72 by the annual interest rate: at 7% annual return, your money doubles in approximately 72 ÷ 7 = 10.3 years.

Does compound interest account for inflation?

No. Nominal compound interest reflects gross dollar amounts. To find your real purchasing power, subtract expected inflation from your nominal interest rate (e.g., 7% return minus 2.5% inflation gives a 4.5% real annual rate).

How does APY differ from APR?

Annual Percentage Rate (APR) is the simple nominal interest rate before compounding is applied. Annual Percentage Yield (APY) represents the true effective annual yield that accounts for the compounding frequency.