Compound interest pays you interest on your interest, so a balance grows faster the longer it is left alone. Enter a starting amount, a rate and a term below, and add a regular deposit if you are saving monthly rather than investing a lump sum once.
Someone is checking a savings or investment plan: they have a starting amount, a rate they have been quoted, and a number of years, and they want to know what it becomes — usually with a monthly contribution on top.
Simple interest pays you a fixed amount every year based on the money you originally put in, and that amount never changes. Compound interest pays you interest on the balance as it stands, which includes interest you have already been paid. The difference is invisible in year one and enormous by year thirty.
The practical consequence is that the growth is not a straight line. It is an exponential curve, which looks almost flat for the first few years and then bends sharply upward. A 6% return on $10,000 adds $600 in year one; by year twenty the same 6% is adding more than $1,900 in a single year, because it is being paid on a much larger balance.
This is why the length of the term matters more than the rate for most realistic plans. Doubling the rate doubles the yearly interest; extending the term does not double anything, it moves you further along a curve that keeps steepening.
Simple interest is the comparison case: the same percentage applied to the same original amount every year, with nothing reinvested. It has no exponent in its formula and its graph is a straight line, and it is what you effectively get if you take the interest out each year instead of leaving it in.
The gap between the two is the cost of not reinvesting. $5,000 at 4% simple interest for 30 years grows to $11,000. The same $5,000 at 4% compounded annually grows to $16,217. Nothing about the rate changed — only whether the interest was allowed to earn interest of its own.
Compounding more often gives a slightly higher result at the same nominal rate, because interest starts earning interest sooner. $10,000 at 6% for ten years becomes $17,908.48 compounded annually, $18,140.18 compounded quarterly, and $18,193.97 compounded monthly. Daily compounding reaches $18,220.29 — $26.32 more than monthly over the whole decade.
The gap narrows because of diminishing returns: going from annual to monthly captures most of the available benefit, and going from monthly to daily captures very little. If a bank advertises a higher rate for daily compounding, the rate difference is almost always doing more work than the frequency.
The number that lets you compare fairly across frequencies is the effective annual rate — what the nominal rate works out to once compounding is included. At 6% nominal, monthly compounding is an effective 6.17%, and daily is 6.18%.
This tool assumes a rate that never changes, deposits that stay the same, and no tax. Real accounts fail all three: rates move, contributions get raised with a salary, and interest is taxed as it is earned in most taxable accounts. Treat the answer as the shape of the outcome rather than a prediction.
It also assumes deposits go in at the end of each period. If you deposit at the beginning, each contribution earns one extra period of interest, and the total comes out slightly higher than shown here. For an ordinary savings plan the difference is small; for large regular contributions over a long term it is not.
A = P(1 + r/n)^(nt) + PMT × [ ((1 + r/n)^(nt) − 1) ÷ (r/n) ]
The first term is your starting amount growing on its own. The second is the deposits: it is the standard future-value-of-an-annuity formula, and it is why the deposit input is "per period" and not "per month" — the two are the same only when compounding is monthly.
You put $10,000 into an account paying 6% a year, compounded monthly, and leave it for 10 years without adding anything. The balance at the end is $18,193.97, of which $10,000 is your original money and $8,193.97 is interest. Notice that the interest earned is nearly as large as the amount you put in — and that none of it required a further deposit.
Now start with $5,000 at 7% compounded annually for 20 years, and add $1,200 at the end of every year. The balance reaches $68,543.01. You paid in $29,000 in total — $5,000 at the start plus twenty deposits of $1,200 — so $39,543.01 of the final figure is growth. The deposits contribute far more than the starting amount, which is the usual pattern: regular contributions matter more than a good entry price.
A five-year plan: $1,000 to start, $200 deposited every month, at 4% compounded monthly. The balance after five years is $14,480.79, against $13,000 paid in. Only $1,480.79 is interest, because five years is not long enough for compounding to do much of the work. That is the honest result of a short horizon, and it is why the term input moves the answer more than the rate does.
| Year | Balance | Interest so far |
|---|---|---|
| 1 | $10,616.78 | $616.78 |
| 2 | $11,271.60 | $1,271.60 |
| 3 | $11,966.81 | $1,966.81 |
| 4 | $12,704.89 | $2,704.89 |
| 5 | $13,488.50 | $3,488.50 |
| 6 | $14,320.44 | $4,320.44 |
| 7 | $15,203.70 | $5,203.70 |
| 8 | $16,141.43 | $6,141.43 |
| 9 | $17,136.99 | $7,136.99 |
| 10 | $18,193.97 | $8,193.97 |
More than most people expect, and it is the input with the most leverage. $10,000 at 6% compounded monthly reaches $18,193.97 after ten years and $32,071.35 after twenty. The second decade adds more than the first, because the balance it is working on is larger. Delaying by five years costs you the steepest part of the curve.
For a lump sum, multiply the principal by (1 + r/n) raised to the power of nt, where r is the annual rate as a decimal, n is the number of compounding periods per year, and t is the term in years. For regular deposits, add the future value of an annuity: the deposit multiplied by ((1 + r/n)^(nt) − 1) divided by (r/n).
It matters, but less than most people expect, and it saturates. $10,000 at 6% over ten years gives $17,908.48 annually, $18,193.97 monthly, and $18,220.29 daily. Monthly captures most of the difference from annual; daily adds $26.32 on top over the full ten years. The rate matters considerably more than the frequency.
Three usual reasons: the bank compounds daily but credits monthly, the quoted rate is an effective annual rate rather than a nominal one, or the bank rounds the balance at each period instead of carrying full precision. Rounding each period is the largest of the three and always produces a slightly lower figure.