🎯 In 30 seconds: Five small formulas answer most everyday money questions: how much did that change, how much will this grow, how long to double, what does this loan really cost, and when does a purchase pay for itself. A phone calculator is all you need.
1. Percent change
In words: new minus old, divided by old, times 100.
Example: rent goes from $1,500 to $1,620. ($1,620 − $1,500) ÷ $1,500 = 0.08, so an 8% increase.
Watch the trap: a 50% drop needs a 100% gain to recover. $100 falls 50% to $50; a 50% gain from there only gets you to $75.
2. Compound interest
In words: start amount times (1 + rate) multiplied by itself once for each year. Interest earns interest.
Example: $5,000 at 5% a year for 10 years. 1.05 multiplied by itself 10 times is about 1.629, so $5,000 × 1.629 = about $8,144. Simple interest (no compounding) would give $5,000 + 10 × $250 = $7,500. The extra $644 is interest on interest, and the gap widens every year.
The same math works against you on debt, which is why a credit card balance left alone grows faster than people expect.
3. The Rule of 72
In words: 72 divided by the yearly rate gives the rough number of years to double.
| Rate | Years to double |
| 3% | about 24 |
| 6% | about 12 |
| 8% | about 9 |
| 24% (a credit card) | about 3 |
It works for inflation too: at 3% inflation, prices double in about 24 years. It is an estimate that works best between about 2% and 15%.
4. The true cost of a loan
In words: monthly payment times number of payments, minus the amount borrowed, equals the total interest. The payment itself comes from a standard formula: loan × r ÷ (1 − (1 + r) raised to the power of −n), where r is the yearly rate divided by 12 and n is the number of months. Any online loan calculator does this for you.
Example: a $25,000 car loan at 7%.
| Term | Monthly payment | Total interest |
|---|---|---|
| 60 months | $495.03 | $4,701.80 |
| 72 months | $426.23 | $5,688.21 |
The longer loan lowers the payment by about $69 a month but costs about $986 more. A dealer quoting only the monthly payment is showing you half the picture.
5. Break-even of a purchase
In words: upfront cost divided by the saving per use (or per month) equals how many uses (or months) until it pays for itself.
Example: a $150 espresso machine. A café drink costs $4.50; making it at home costs about $0.50. The saving is $4 per cup, so $150 ÷ $4 = 37.5. After 38 cups the machine is free, and every cup after that saves $4. If you would only use it twice a month, that is a year and a half to break even, and a different answer.
Same idea for a $120 smart thermostat that cuts the energy bill by $10 a month: $120 ÷ $10 = 12 months.