Guide

Compound Interest Formula

The compound interest formula is a quick way to estimate a future balance from a starting amount, an annual rate, a compounding frequency, and time. Use it to sanity-check projections before you plug numbers into a calculator.

Published: March 11, 2025 · Updated: December 21, 2025 · By FinToolSuite Editorial

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Plug the formula inputs into the calculator and see timelines, totals, and charts.

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Quick answer

A = P(1 + r/n)^n·t

A is the ending balance after compounding. Need APR vs APY? See APR vs APY explained.

Disclaimer

Educational purposes only; not financial advice. Results are illustrative; real returns vary and investments can go down as well as up. Fees, taxes, inflation, and account rules vary by provider and country.

Formula variables

A: Future value (ending balance)
P: Principal (starting amount)
r: Annual interest rate (decimal, so 5% = 0.05)
n: Number of compounding periods per year
t: Time in years

Worked example (lump sum)

P = £1,000, r = 0.05, n = 12, t = 10.

Substitute into A = P(1 + r/n)^n·t:

A = 1,000 × (1 + 0.05/12)^12×10

A ≈ 1,000 × (1.0041667)¹²⁰ ≈ £1,648

Total interest ≈ £1,648 − £1,000 = £648

Try these inputs in the compound interest calculator.

Why compounding frequency matters

More frequent compounding adds interest slightly more often, which can nudge the ending balance higher. The difference is small over short periods and grows over longer periods.

Using the same example (P £1,000, r 5%, t 10 years):

n (per year)	Approx. A
1 (yearly)	~£1,629
12 (monthly)	~£1,648
365 (daily)	~£1,650

Common pitfalls

Using 5 instead of 0.05 for the rate.
Mixing APY and nominal rates without adjusting n or r.
Not aligning time units (entering months in t when the rate is annual).

FAQs

What is the compound interest formula?

A = P(1 + r/n)^n·t, where A is the ending balance and P is the starting amount.

What do P, r, n, and t mean?

P is principal, r is annual rate (decimal), n is compounding periods per year, t is years.

Is r the APR or APY?

Use the nominal annual rate for r. APY already reflects compounding. See APR vs APY.

How do I choose n?

Match n to the compounding schedule: yearly (1), monthly (12), daily (365), etc.

How do monthly contributions fit into the formula?

The lump-sum formula above doesn’t include contributions. Use a calculator to add deposits on a schedule.

Does daily compounding make a big difference?

Usually it’s a small lift over monthly for modest rates and timelines; the gap grows slowly with more time.

What if I only have months, not years?

Convert months to years for t (e.g., 18 months = 1.5 years) to align with an annual rate.

Run your scenarios

Try monthly vs yearly compounding in the calculator to bracket your illustrative results.

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