Find the exact time for an investment to triple.
The same logarithmic method as doubling time, solved for a threefold increase instead of twofold.
Years: ln(3) ÷ ln(1 + rate)
Tripling time is how long an investment takes to reach three times its starting value at a steady annual return. This calculator computes it exactly with logarithms, as the precise counterpart to the Rule of 114 shortcut.
Tripling is a useful benchmark for medium to long goals. Parents saving for a child's college in 12 to 15 years, or someone planning a large purchase over a decade, often want to know whether a sum invested today could triple by then. Knowing the exact time also helps you judge marketing claims and compare products.
Like doubling time, tripling time depends only on the rate, not on how much you invest.
1. Take the annual return R in percent, compounded yearly.
2. Compute the growth factor 1 + R ÷ 100.
3. Take natural logarithms: ln 3 is about 1.0986.
4. Divide: tripling time = ln 3 ÷ ln(1 + R ÷ 100).
5. Compare with the Rule of 114 estimate, 114 ÷ R.
6. To find the rate needed to triple in N years, compute R = (3^(1/N) − 1) × 100.
Since doubling time is ln 2 ÷ ln(1 + r) and tripling time is ln 3 ÷ ln(1 + r), their ratio is ln 3 ÷ ln 2, about 1.585, at any rate. So if money doubles in 8 years, it triples in about 12.7 years. Put another way, once money has doubled, going from twice to three times takes only ln 1.5 ÷ ln 2, about 0.58, of a doubling time. Growth from 2× to 3× is a 50% increase, which is smaller than the 100% increase from 1× to 2×, so it takes less time.
The Rule of 114 is tuned for rates near 8%. At 10%, it gives 11.4 years against an exact 11.53. At 18%, it gives 6.33 against an exact 6.64, and the gap widens at higher rates. For a goal with a fixed date, such as a college admission, a few months can matter. The exact calculation also lets you answer the reverse question precisely: to triple money in 10 years, you need (3^(1/10) − 1), or about 11.6% a year.
The formula assumes a single lump sum, a constant yearly rate and no withdrawals, taxes or fees along the way. Deposits and small savings schemes come close to this, though their compounding may be quarterly, which shortens the time slightly. Market-linked investments do not grow smoothly, so the tripling time is what happens if their average return equals your assumption. Tax on interest reduces the effective rate, so after-tax tripling time for an FD is noticeably longer than the pre-tax figure.
Mohan is setting aside a lump sum for his daughter's higher studies and wants to know exactly how long it takes to triple if it earns 10% a year.
Answer: Exact tripling time 11.527 years
Assuming tripling takes 1.5 times the doubling time; it takes about 1.58 times.
Assuming the stretch from double to triple takes as long as the first doubling; it takes less.
Using pre-tax FD rates for a post-tax plan.
Relying on the Rule of 114 at high rates.
Expecting a volatile investment to triple exactly on schedule.
Checking whether a lump sum can triple before a child's college admission.
Finding the return needed to triple money within a set number of years.
Evaluating 'money triples' claims in investment advertisements.
Illustrating logarithms and growth ratios in maths classes.
Why does tripling take longer than doubling by more than 50%?
At a steady compound rate, tripling time = ln 3 ÷ ln(1 + r), which is always about 1.585 times the doubling time, because ln 3 ÷ ln 2 ≈ 1.585. So going from double to triple takes about 58% of a doubling period: at 8% a year, doubling takes about 9 years and tripling about 14.3 years.