08 / MONEY MATH
Compound interest,
made visible.
Compounding means growth is calculated on an amount that already includes earlier growth. The arithmetic is simple; choosing realistic assumptions is the hard part.
THE BASIC MODEL
Each period starts from a new total.
With a fixed rate compounded once per period and no deposits or withdrawals, the future value is the starting amount multiplied by one plus the rate, raised to the number of periods. A 100-unit starting balance at 5% for one year becomes 105 units. The next year's 5% is applied to 105, not the original 100.
future value = starting amount × (1 + rate per period)number of periodsFor more frequent compounding, use the rate and number of periods that match the contract. A quoted annual percentage rate may not be the same thing as the effective annual yield. Fees, taxes, and variable rates can make the tidy formula a poor description of an actual account.
A QUICK ESTIMATE
The Rule of 72 is a shortcut, not a forecast.
Divide 72 by an annual percentage rate to estimate how many years a balance might take to double under steady compounding. At 6%, the rough answer is 12 years. The shortcut is most useful for quick mental comparisons around ordinary positive rates; it becomes less accurate at extreme rates and says nothing about whether a rate will persist.
Inflation changes what a future amount can buy. A balance that doubles in nominal currency over a period does not mean its purchasing power doubled. To think about purchasing power, compare the growth rate with inflation over the same interval, while remembering that personal costs can rise differently from a general price index.
REGULAR DEPOSITS / TIMING MATTERS
Contributions add another moving part.
When money is added regularly, each deposit has its own time to grow. A deposit made at the beginning of a period compounds for one more period than a deposit made at the end. Payment frequency, contribution size, fees, rate changes, and withdrawals all alter the result.
For a fair comparison, hold the assumptions visible: starting amount, contribution schedule, effective rate, compounding frequency, fees, tax treatment, and time horizon. A graph can make exponential curves feel inevitable, but the inputs are scenarios, not guarantees.
THE OTHER SIDE / BORROWING
Compounding can grow debt too.
If unpaid interest is added to the amount owed, future interest can be charged on that larger balance. Fees and variable rates may add further complexity. When comparing borrowing options, look at the total repayment, the rate definition, payment timing, fees, and what happens if a payment is late—not only the monthly amount shown in an advertisement.
Small differences in assumptions can produce very different long-range results. Use a calculator to explore “what if” cases, then verify real terms in the relevant agreement. For personal decisions, consider qualified, independent advice suited to your country and circumstances.
The Economics & Finance Lab explores interest, inflation, and simple decision models. This guide is for learning the math, not recommending an investment or loan.