SHIP'S INSTRUMENTS

Compound interest calculator

Which grows more: money you already have, invested once and left alone, or a steady monthly contribution? Enter a starting lump sum, a monthly amount, an expected return, and a horizon. The calculator plots all three scenarios - lump sum only, monthly only, and both together - and shows where they cross.

Compound interest

Compare a lump sum left alone, steady monthly contributions, and both together.

Set either amount to zero to look at just one scenario.

How it's calculated

  1. Everything compounds monthly, so the monthly rate r is the annual return divided by 12 and n is the number of months.
  2. A lump sum L left alone grows to L × (1 + r)n. Monthly contributions P, added at the end of each month, grow to P × ((1 + r)n − 1) / r. "Both together" is simply the two added up.
  3. Growth is the ending balance minus what you put in - the lump sum, the contributions, or both. The crossover note finds the first year the monthly plan's balance passes the lump sum's. The Rule of 72 divides 72 by the annual return to estimate the doubling time.

Worked example

At 7% over 20 years, $40,000 invested once grows to about $161,550, while $500 a month grows to $260,463 - though the monthly plan puts in $120,000 against the lump sum's $40,000. The monthly plan overtakes the lump sum in year 10. Doing both ends at about $422,013.

Frequently asked

Lump sum or monthly contributions - which is better?

Per dollar invested, the lump sum wins: it compounds from day one, so $40,000 more than quadruples in 20 years at 7%. But a monthly plan keeps adding new money, so over a long enough horizon its total pulls ahead - here in year 10. The real answer is to do both: invest what you have now, then keep contributing.

What return should I use?

The US stock market has averaged around 10% a year before inflation over long periods and roughly 7% after it, which is why 7% is the default. A savings account or bonds will be far lower. Pick the number that matches where the money will actually sit, and try a lower one to see how sensitive the result is.

Is the result adjusted for inflation?

Only if you enter a real return. Using 7% instead of 10% is the usual way to get an answer in today's dollars.

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