How Long to Double Money at 5 Percent?

Rule of 72 vs the Exact Formula

The Rule of 72 is a mental-math shortcut: divide 72 by the annual interest rate to estimate how many years it takes to double. At 5 percent, 72 divided by 5 gives 14.4 years. The actual formula, t = ln(2) / ln(1 + r), produces 14.21 years when r is 0.05 and interest compounds annually. The rule overshoots by about two months at this rate.

That small gap exists because the Rule of 72 is an approximation that works best near 8 percent, where it is almost perfectly accurate. At lower rates it slightly overstates the time, and at higher rates it slightly understates it. For a quick estimate when comparing savings accounts or investment options, the rule is reliable enough. For precise planning, the calculator uses the exact logarithmic formula and shows how the two results diverge. Daily compounding shortens the true doubling time further, to approximately 13.9 years at an illustrative 5 percent, because interest earns interest more frequently.

What Happens After the First Doubling

Doubling once is interesting. Doubling repeatedly is where compounding becomes powerful. At an illustrative 5 percent, $5,000 becomes $10,000 in about 14 years, then $20,000 around year 28, and roughly $40,000 near year 42. Each doubling adds the same percentage gain, but the dollar amount doubles too. The jump from $5,000 to $10,000 adds $5,000. The jump from $10,000 to $20,000 adds $10,000. Same rate, same timeframe, twice the dollars.

This is why time in a savings account matters more than timing. A 25-year-old who deposits $5,000 today and earns an illustrative 5 percent has roughly 40 years until age 65, enough for nearly three full doublings. The same deposit made at 40 allows only about one and a half doublings. The Rule of 72 calculator lets you test any rate to see how many doublings fit inside your own savings horizon and how the exact formula compares to the shortcut.

The Rule of 72 is an approximation. For exact results, the calculator uses the logarithmic doubling formula with the compounding frequency you select.