The Beginner's Guide to Financial Calculators: Loans, Interest, and Investment Math
How mortgage payments, compound interest, and the Rule of 72 are actually calculated, with real worked examples.
Almost every financial decision — buying a house, saving for retirement, paying off a credit card — comes down to a handful of formulas repeated with different numbers. Once you understand the core mechanics, every calculator on this site (and every bank's amortization table) stops being a black box.
Simple interest vs. compound interest
Simple interest only ever applies to the original amount you started with. If you deposit $5,000 at 5% simple interest for 3 years, you earn 5,000 × 0.05 × 3 = $750, every year the same $250.
Compound interest is different: each period's interest gets added to the balance, so the next period earns interest on the interest too. That's why a $10,000 investment growing at 7% annually for 20 years doesn't just double or triple — using A = P(1+r)ⁿ, it grows to 10,000 × (1.07)^20 ≈ $38,697, nearly 4x the original principal, without a single extra dollar contributed.
The gap between simple and compound interest widens every year, which is exactly why starting to invest early matters more than the exact rate of return.
How a mortgage payment is actually calculated
A 30-year mortgage isn't just "loan amount divided by 360 months." Lenders use the amortizing loan formula:
M = P × [r(1+r)ⁿ] / [(1+r)ⁿ − 1]
where P is the principal, r is the monthly interest rate (annual rate ÷ 12), and n is the number of payments. For a $300,000 loan at 6.5% over 30 years, r = 0.065/12 ≈ 0.005417 and n = 360, which works out to a monthly payment of $1,896.20 — and over the life of the loan, roughly $382,633 of that is interest, not principal.
This is also why paying even a little extra toward principal early in a loan saves so much interest: early payments are mostly interest, so extra principal payments compound in your favor for the entire remaining term.
The Rule of 72
Want a quick mental estimate of how long it takes an investment to double, without doing the exponent math? Divide 72 by the annual interest rate. At 8% annual growth, money doubles in roughly 72 / 8 = 9 years. It's an approximation (most accurate between 6-10% rates), but it's close enough for back-of-envelope planning.
Where to go from here
- Use the mortgage calculator to see your own numbers with real property values and rates
- Try the compound interest calculator to model a retirement savings plan with monthly contributions
- Check the Rule of 72 calculator before committing to any "guaranteed doubling" investment pitch — if the math doesn't check out, be skeptical
None of these calculations require anything beyond arithmetic you learned in school; the only trick is knowing which formula applies to which situation.