Compound Interest Calculator — Free Tool

How to Use This Compound Interest Calculator

Enter your initial investment (principal), monthly contribution, estimated annual interest rate, time period in years, and compounding frequency (daily, monthly, quarterly, semi-annually, or annually).

The calculator converts your monthly contribution to match the compounding frequency, then iterates period by period: each period, interest is calculated on the current balance, added to the balance, and then the contribution is added.

This period-by-period approach matches how real accounts accrue interest and ensures accuracy even when contribution and compounding frequencies differ.

The rate variance feature runs the same calculation at higher and lower rates so you can see best-case and worst-case scenarios.

What is Compound Interest Calculator?

A compound interest calculator shows how an investment or savings account grows over time when interest is reinvested and earns its own interest. Albert Einstein reportedly called compound interest "the eighth wonder of the world" — whether or not he actually said it, the math is remarkable. Small differences in rate, time, or contribution amount create enormous differences in final value over decades. This tool models the standard compound interest formula used by investor.gov and financial textbooks worldwide. You enter an initial investment, a monthly contribution (positive for deposits, negative for withdrawals), an estimated annual interest rate, the number of years, and the compounding frequency. The calculator then shows your future value, total contributions vs total interest earned, a rate variance range for optimistic and conservative scenarios, a growth chart, and a year-by-year breakdown table. All math runs in your browser — nothing is sent to a server.

Formula

Basic compound interest (no contributions):
A = P × (1 + r/n)^(nt)

With regular contributions (ordinary annuity):
A = P × (1 + r/n)^(nt) + PMT × [((1 + r/n)^(nt) − 1) / (r/n)]

Where:
P   = initial principal (initial investment)
PMT = contribution per compounding period
r   = annual interest rate (decimal)
n   = compounding periods per year
t   = time in years

Formula Explained

The first term, P × (1 + r/n)^(nt), calculates how the initial lump sum grows. Each compounding period, the balance is multiplied by (1 + r/n) — the per-period growth factor. After nt total periods, this multiplication has been applied nt times, which is why we raise it to that power. The second term handles regular contributions. Each contribution also grows by compound interest, but for a shorter time since each is added later. The summation of all these growing contributions forms a geometric series, and the closed-form solution is PMT × [((1 + r/n)^(nt) − 1) / (r/n)]. This assumes contributions are made at the end of each period (ordinary annuity). When the interest rate is 0, the formula simplifies to just adding up contributions without growth.

Example

Initial investment: $10,000 Monthly contribution: $100 Annual interest rate: 6% Time: 10 years Compounding: Monthly Calculations: r/n = 0.06/12 = 0.005 nt = 12 × 10 = 120 periods Contribution per period = $100 Lump sum growth: $10,000 × (1.005)^120 = $18,193.97 Contribution growth: $100 × [((1.005)^120 − 1) / 0.005] = $16,387.93 Future Value: $18,193.97 + $16,387.93 = $34,581.90 Total contributed: $10,000 + ($100 × 120) = $22,000.00 Total interest earned: $34,581.90 − $22,000.00 = $12,581.90 Verify: investor.gov shows $34,581 for these inputs — ✓

Tips & Best Practices

✓Start early: 10 years of compounding can be worth more than the contributions themselves.
✓Use the Rule of 72 to quickly estimate doubling time: 72 ÷ rate% = years to double.
✓Even small monthly contributions add up dramatically over 20-30 years due to compounding.
✓Compare compounding frequencies — monthly vs annually makes a meaningful difference over long periods.
✓Use the rate variance feature to plan for both optimistic and conservative outcomes.

Common Use Cases

•Planning retirement savings by projecting 401(k) or IRA growth
•Comparing savings account APY offers from different banks
•Teaching students how exponential growth works in finance
•Estimating how long it takes to reach a savings goal
•Modeling investment growth scenarios with different contribution amounts

Frequently Asked Questions

Compound interest is interest calculated on both the initial principal and the accumulated interest from previous periods. Unlike simple interest (which is only on the principal), compound interest grows exponentially over time. For example, $1,000 at 10% simple interest earns $100/year forever. With compound interest, year 1 earns $100, year 2 earns $110 (10% of $1,100), year 3 earns $121, and so on—each year earns more than the last.

Free Compound Interest Calculator