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What is Compound Interest?

Compound interest is the interest you earn on your initial investment (the principal) plus the interest you've already earned. In other words, it's "interest on interest." This creates a snowball effect, causing your wealth to grow at an accelerating rate over time.

Imagine you invest $1,000 at a 10% annual return. After the first year, you have $1,100. In the second year, you earn 10% on the new, larger amount of $1,100, which is $110 in interest (compared to just $100 in the first year). This cycle continues, with your investment generating ever-increasing returns each year.

Visualizing the Power of Compounding

The difference between simple and compound interest may seem small at first, but over time, it becomes immense. This animation shows the growth of $1,000 over 30 years at a 10% annual rate.

Compound Growth

$1,000

Year

0

Simple Growth

$1,000

Rent vs Buy — Overview

Compare long‑term net worth, not just monthly payments.

Buying builds equity through principal paydown and appreciation. Renting frees cash to invest. Compare net worth over time, not monthly payments:

  • Buy Net = Home value × (1 − selling %) − Remaining mortgage − Closing.
  • Rent Net = Invested down payment + invested savings vs owning.
  • Tax benefit reduces owner cost; it isn’t added as cash at sale.
Quick Visual
Buy (illustrative)Rent (illustrative)
Illustrative only — not using your inputs.

Assumptions & Methodology

How each scenario is simulated under the hood.

Buying

  • Fixed-rate mortgage amortization (monthly).
  • Appreciation compounded monthly (or annual).
  • Costs: mortgage + property tax + insurance + maintenance.
  • Tax benefit = (interest + property tax) × marginal rate.
  • Sale net = value × (1 − sell %) − mortgage − closing.

Renting

  • Down payment (and closing) invested up front.
  • Savings vs owning invested as monthly contributions.
  • Return compounded monthly (or annual).
  • Rent escalates annually by chosen rate.

When Each Tends To Win

Buying often wins when…

  • You’ll stay long enough to spread closing/selling costs.
  • Mortgage rate is favorable vs expected investment return.
  • Local appreciation is robust and supply is constrained.
  • You plan to rent out later or house‑hack (offsets costs).

Renting often wins when…

  • Your time horizon is short (transaction costs dominate).
  • Rent is much cheaper than owning comparable quality.
  • You can reliably invest the difference at higher returns.
  • Maintenance/insurance/tax burdens are unusually high.

Key Sensitivities

  • Time horizon: most impactful factor; try 3 vs 10 years.
  • Rent vs own delta: gap between monthly rent and owner outflow.
  • Investment return vs mortgage rate: opportunity cost.
  • Appreciation and selling costs: exit matters.
  • Maintenance/property tax: varies by market and property type.

Key Financial Facts & Rules of Thumb

The S&P 500 Average Return

Historically, the average annual return for the S&P 500 (a benchmark for the US stock market) is around **10-12%**. After adjusting for inflation, this is often cited as **7-8%**. Our calculator defaults to 7% as a realistic long-term expectation for a diversified portfolio.

The Rule of 72

The "Rule of 72" is a quick, useful shortcut to estimate how long it will take for an investment to double in value. Simply divide 72 by your annual interest rate.

72 / (Interest Rate %) = Years to Double

For example, an investment with an 8% annual return will double approximately every 9 years (72 / 8 = 9).

The Formula Explained

A = P(1 + r/n)nt

  • A = The future value of the investment/loan, including interest.
  • P = The principal amount (the initial amount of money).
  • r = The annual interest rate (in decimal form).
  • n = The number of times that interest is compounded per year.
  • t = The number of years the money is invested for.

Why Starting Early is Crucial

The most important factor in the compound interest equation is **time**. The longer your money has to grow, the more dramatic the effects of compounding will be.

Someone who starts investing $500 a month at age 25 will have significantly more money by age 65 than someone who starts investing $1,000 a month at age 45, even though they invested less of their own money. The extra 20 years of growth allow the interest to compound to a much greater degree. Our calculator can help you visualize this "cost of waiting."