Compound Interest

Money that earns interest on its interest grows faster every year. Find what an amount grows to, how much you need to start with, what rate it takes or how long it takes — and add a regular deposit to see what saving every month or year adds up to, or what you need to save for a goal.

FinanceInterestSavingAnnuity

Inputs

Interest added

Input examples

Choose how often the interest is added, then click Solve next to the quantity you want to find: it moves into the result below. The rate is the yearly (nominal) rate in %. The regular deposit is optional (0 for none); a deposit at the start of a period earns interest for that period too. For education only — not financial advice; real accounts can have fees and taxes.

Currency

Starting amount P — in €

Interest rate r — % per year

Time t — years

Regular deposit D — per month, € (0 for none)

Final amount A — in €

Deposits

What is Compound Interest?

With simple interest you only earn interest on the money you put in. With compound interest the interest is added to the balance, so next time you also earn interest on the interest. The balance grows by the same percentage every year — slowly at first, then faster and faster. How often interest is added matters a little; the effective annual rate tells you what you really earn per year.

With regular deposits every deposit starts its own little snowball. Added up, this series of equal payments is an annuity, with a neat closed formula. Over long periods most of the final amount can come from interest rather than from what you put in, which is why starting early matters so much.

rule of 72doubles in ≈ 72 / r years

5% monthly= 5.12% a year

€200/month30 y at 6% ≈ €201k

depositedonly €72k of it

Growth Over Time

balance

balance with compound interest

simple interest (no interest on interest)

your result

Result

Enter the values above

Year by Year

Year	Balance	Put in so far	Interest that year	Total interest

Worked Techniques

The Rule of 72 and the Effective Rate

A quick estimate of how long it takes for money to double (exact: ln 2 / ln(1 + r)). The effective rate compares offers with different compounding: 5% paid monthly is 5.116% a year.

Example: at 6%: 72 / 6 = 12 years (exact: 11.9 years).

Future Value of Regular Deposits

N equal deposits D, each earning interest from the moment it is paid in. Use the rate per period i and the number of deposits N; paid at the start of each period, multiply by (1 + i).

Example:

Saving for a Goal

Rearranged, the formula gives the deposit you need to reach a target amount in a given time.

Example: 100 000 in 15 years at 4%: about 406 a month.

Sources & Verification

References

R. A. Brealey, S. C. Myers & F. Allen, Principles of Corporate Finance, 13th ed., McGraw-Hill Education, 2020 — Ch. 2 (How to Calculate Present Values: compound interest and annuities).