Skip to content

Compound Interest Calculator — Step-by-Step Solutions

The Compound Interest Calculator shows how your money grows with the power of compounding. It uses the formula A = P(1 + r/n)^(nt) to compute future value across different compounding frequencies.

Enter your principal, interest rate, and time period to see projected growth. The calculator supports four modes: future value, with regular contributions, time to reach a target, and side-by-side frequency comparison.

Your calculations will appear here

How to Use the Compound Interest Calculator

  1. Enter the initial principal (starting amount).
  2. Enter the annual interest rate as a percentage.
  3. Select the investment period in years.
  4. Choose the compounding frequency: annually, semi-annually, quarterly, monthly, or daily.
  5. Click "Calculate" to see the final amount and total interest earned.

Formula and Theory

The compound interest formula is: A = P * (1 + r/n)^(n * t), where A is the final amount, P is the principal, r is the annual interest rate as a decimal, n is the number of compounding periods per year, and t is the time in years.

Compound interest differs from simple interest in that interest is earned on previously accumulated interest, not just on the principal. This creates exponential growth. The more frequently interest is compounded, the higher the effective yield.

The Rule of 72 provides a quick estimate of doubling time: divide 72 by the annual interest rate to get the approximate number of years for the investment to double. At 6% interest, the principal doubles in roughly 12 years.

Worked Examples

Example 1: Monthly compounding

Problem: Invest 10,000 at 5% annual interest, compounded monthly, for 10 years.

Solution: A = 10,000 * (1 + 0.05/12)^(12 * 10) = 10,000 * (1.004167)^120 = 16,470.09.

Answer: 16,470.09 (interest earned: 6,470.09)

Example 2: Annual compounding

Problem: Invest 5,000 at 8% annual interest, compounded annually, for 20 years.

Solution: A = 5,000 * (1 + 0.08)^20 = 5,000 * 4.66096 = 23,304.79.

Answer: 23,304.79 (interest earned: 18,304.79)

Example 3: Comparing compounding frequencies

Problem: Invest 20,000 at 6% for 15 years: annual vs daily compounding.

Solution: Annual: 20,000 * 1.06^15 = 47,931.64. Daily: 20,000 * (1 + 0.06/365)^(365*15) = 49,165.80.

Answer: Daily compounding yields 1,234.16 more

Example 4: Real-world: retirement savings

Problem: Starting at age 25 with 1,000, contributing nothing more, at 7% annual interest compounded annually, what is the balance at age 65?

Solution: A = 1,000 * (1.07)^40 = 1,000 * 14.974 = 14,974.

Answer: 14,974 after 40 years (the original 1,000 grew nearly 15-fold)

Frequently Asked Questions

What is the difference between simple and compound interest?
Simple interest is calculated only on the original principal. Compound interest is calculated on the principal plus any accumulated interest. Over time, compound interest grows exponentially while simple interest grows linearly.
What is the Rule of 72?
It is a quick estimation: divide 72 by the interest rate to find the approximate number of years for an investment to double. At 8% interest, the doubling time is roughly 72/8 = 9 years.
How does compounding frequency affect returns?
More frequent compounding produces higher returns because interest is earned on interest more often. The difference is most noticeable at higher interest rates and over longer time periods.
What is continuous compounding?
Continuous compounding is the theoretical limit of compounding frequency, where interest is compounded at every instant. The formula becomes A = P * e^(r*t). In practice, daily compounding approximates continuous compounding very closely.
Why is compound interest called the "eighth wonder of the world"?
This phrase, often attributed to Albert Einstein, highlights the power of exponential growth. Small differences in interest rate or time can produce dramatic differences in final value. Starting early and letting compound interest work over decades is one of the most effective strategies for building wealth.

Related Finance Calculators

dollar

Mortgage Calculator

Calculate monthly mortgage payments, total interest, and amortisation schedules. Compare refinance options and find how much you can afford.

dollar

Margin Calculator

Calculate profit margin, markup, and selling price. Convert between margin and markup percentages. Compare gross and net margins. Free online margin calculator.

dollar

Sales Tax Calculator

Calculate sales tax, find pre-tax prices, and compare tax rates. Includes US state tax rate reference table. Free online sales tax calculator.

dollar

Discount Calculator

Calculate sale prices, find discount percentages, and work out stacked discounts. See how much you save. Free online discount calculator.

dollar

Inflation Calculator

Calculate purchasing power, inflation rates between years, and future value adjusted for inflation. US CPI data from 1913 to 2025. Free online inflation calculator.

dollar

Investment Calculator

Calculate investment growth with monthly contributions. Find future value, required contributions, time to reach goals, and compare scenarios. Free online tool.