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NumLuma›Guides›Money math
Money math guide

Compound Interest: The Math Behind Growth

Compound growth means each period can earn a return on both the original amount and previous growth. Over long periods, that reinvestment can create a large difference compared with simple interest.

Evergreen referenceFormula-focusedRelated calculators included
01

The four main inputs

A basic compound-interest calculation uses principal, interest or growth rate, time and compounding frequency. Principal is the starting amount. The rate describes growth per year. Time determines how long compounding continues.

Compounding frequency describes how often growth is applied. Monthly compounding uses 12 periods per year, while annual compounding uses one.

02

Why time changes the curve

Compounding is exponential rather than linear. A constant percentage applies to a growing balance, so the absolute amount of growth can become larger in later years even when the rate stays unchanged.

This is why comparing only the first year of growth can understate the effect of a long time horizon.

03

Regular contributions change the calculation

A savings plan with monthly contributions has two sources of future value: the starting balance and the stream of later deposits. Each deposit has a different amount of time to grow.

NumLuma’s savings-growth calculator assumes contributions are made at the end of each month. A different deposit schedule will produce a somewhat different result.

04

A projection is not a promise

Compound-interest math can show what would happen at a constant rate, but real investment returns, savings rates, fees, taxes and inflation can vary. Use projections to compare scenarios rather than treating a chosen rate as guaranteed.