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Compound Interest Calculator

Calculate the exponential growth of your investments with custom contributions and interest compounding options.

Calculator Variables

$
$
%
yrs

Calculation Overview

Calculate investment growth using compound interest with our free calculator. Supports custom monthly contributions and compound frequencies.

Mathematical Model & Formula

A = P(1 + r/n)^(nt) + PMT * [((1 + r/n)^(nt) - 1) / (r/n)]

This formula calculates both the compound interest on your initial principal amount and the future value of a series of regular monthly savings contributions (an ordinary annuity) compounded at the same rate.

Variables Defined:
  • A: Ending balance
  • P: Initial principal balance
  • PMT: Periodic payment
  • r: Annual interest rate (decimal)
  • n: Number of compounding periods per year
  • t: Time horizon in years

Worked Example Scenario

Scenario: You invest $10,000 at an 8% annual interest rate, compounded monthly, contributing $500 every month for 10 years.

  1. Initial Principal (P) = $10,000
  2. Monthly Contribution (PMT) = $500
  3. Rate (r) = 0.08, Compounding frequency (n) = 12
  4. Calculate compound principal growth over 10 years: $10,000 * (1 + 0.08/12)^120 ≈ $22,196
  5. Calculate contribution accumulation: $500 * [((1 + 0.08/12)^120 - 1) / (0.08/12)] ≈ $91,473
  6. Add both values: $22,196 + $91,473 ≈ $113,669

Result: Ending investment balance is $113,669, consisting of $70,000 contributions and $43,669 earned interest.

Frequently Asked Questions

What is the frequency of compounding?

The compounding frequency refers to how often interest is calculated and added back to the principal. More frequent compounding (e.g., daily instead of annually) results in slightly higher total interest accrued.

How is compound interest different from simple interest?

Simple interest pays returns only on the original principal. Compound interest accrues on both the initial principal and previously earned interest, accelerating wealth growth exponentially.

Academic & Regulatory References