💰 Financial Math

Interactive calculators for compound interest, savings growth, loans, and more.

📈 Compound Interest Calculator

Starting Amount (Principal) $
Monthly Contribution $/month
Annual Interest Rate 7%
Years 30 yrs
Compound Frequency
Future Value
—
total balance
Total Invested
—
your money in
Interest Earned
—
compound growth
Doubling Time
—
Rule of 72
BALANCE OVER TIME — Principal / Contributions / Interest

💳 How Long to Reach Your Goal?

Savings Goal $
Starting Amount $
Monthly Savings $/month
Annual Interest Rate 5%
Months to Goal
—
—
Total Saved
—
when goal reached
Interest Earned
—
free money!
SAVINGS PROGRESS TOWARD GOAL

🏦 Loan / Mortgage Calculator

Loan Amount $
Annual Interest Rate 6%
Loan Term 5 years
Monthly Payment
—
per month
Total Paid
—
over full term
Total Interest
—
cost of borrowing
PRINCIPAL vs INTEREST PAID OVER TIME
AMORTIZATION SCHEDULE (first 24 months)

📐 Rule of 72

Divide 72 by your annual interest rate to estimate how many years it takes to double your money.

72 ÷ 8% = 9 years to double

🔁 Compound vs Simple

Simple interest: I = P × r × t
Compound interest: A = P(1 + r/n)^(nt)
Compounding re-invests interest — you earn interest on your interest.

$1,000 @ 10% for 10 yrs: Simple = $2,000 · Compound = $2,594

💳 Loan Formula

Monthly payment for a fixed-rate loan:

M = P·r(1+r)ⁿ / ((1+r)ⁿ−1)
r = monthly rate, n = months

⏰ Time Value of Money

A dollar today is worth more than a dollar in the future — because today's dollar can be invested and grow. This is the foundation of all financial math.

$100 today @ 7% = $107 next year = $196 in 10 years

📊 Inflation

Inflation erodes purchasing power. At 3% inflation, prices double roughly every 24 years. Real return = nominal rate − inflation rate.

7% nominal − 3% inflation = 4% real return

🏦 APR vs APY

APR (Annual Percentage Rate) ignores compounding. APY (Annual Percentage Yield) includes it — the number on your savings account is APY.

6% APR monthly = 6.17% APY

🎯 Savings Rate Rule

The most powerful factor in building wealth is your savings rate — the percentage of income you save. Even small increases have a huge long-term effect.

Save 20% instead of 10% → retire ~10 years earlier

📉 Amortization

Early loan payments go mostly toward interest. As the principal shrinks, more of each payment goes to principal. This is why paying extra early saves the most.

Extra $100/month on a 30yr mortgage can save 5+ years
Why learn financial math?

Understanding compound interest, loans, and savings growth lets you make better money decisions — how much to save, whether a loan is worth it, and how to build wealth over time. A small difference in interest rate or years makes a huge difference in outcome.

Key formulas
Compound Interest — A = P(1 + r/n)^(nt) Simple Interest — I = P × r × t Loan Payment — M = P·r(1+r)ⁿ / ((1+r)ⁿ−1) Rule of 72 — Years to double = 72 ÷ interest rate Real Return — nominal rate − inflation rate
Key terms
Principal — the original amount invested or borrowed Interest rate — percentage charged or earned per period Compounding — earning interest on previously earned interest Amortization — gradual loan payoff with each payment covering interest + principal APY — Annual Percentage Yield; accounts for compounding frequency
🎯 Try this challenge

If you invest $1,000 at 7% annual return and add $100 every month, how much will you have in 30 years? Compare that to starting 10 years later with $200/month. Which is more? By how much?

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