About

Miscalculating compound interest leads to retirement shortfalls measured in tens of thousands of dollars. The difference between monthly and annual compounding on a $50,000 deposit at 5% over 30 years exceeds $3,800. This calculator applies the standard compound interest formula with periodic contributions, decomposing results into principal versus earned interest per year. It assumes a fixed rate r and does not model tax withholding or inflation adjustment. For accounts with variable rates, recalculate each time the rate changes using the accumulated balance as the new principal P.

Compounding frequency n matters more than most depositors realize. Daily compounding (n = 365) versus quarterly (n = 4) produces a measurable delta that grows nonlinearly with time. Pro tip: verify whether your bank compounds on actual calendar days or uses a 360-day convention. This tool uses exact n periods per year as selected.

Formulas

The future value of a lump-sum deposit with regular periodic contributions under compound interest:

A = P(1 + rn)^nt + PMT × (1 + rn)^nt − 1rn

Where A = future value (total balance). P = initial principal deposit. r = annual nominal interest rate (decimal). n = number of compounding periods per year. t = number of years. PMT = periodic contribution amount (added each compounding period).

The effective annual rate (APY) is computed as:

APY = (1 + rn)ⁿ − 1

Total interest earned is simply I = A − P − (PMT × n × t). When r = 0, the formula degenerates to simple accumulation: A = P + PMT × n × t.

Reference Data

Compounding	n (per year)	$10,000 at 5% / 10 yr	$10,000 at 5% / 20 yr	$10,000 at 5% / 30 yr	Effective Annual Rate
Annually	1	$16,288.95	$26,532.98	$43,219.42	5.0000%
Semi-Annually	2	$16,386.16	$26,850.64	$43,997.90	5.0625%
Quarterly	4	$16,436.19	$27,014.85	$44,402.13	5.0945%
Monthly	12	$16,470.09	$27,126.40	$44,677.44	5.1162%
Weekly	52	$16,486.08	$27,178.87	$44,806.90	5.1246%
Daily	365	$16,486.65	$27,181.56	$44,816.81	5.1267%
Continuous	∞	$16,487.21	$27,182.82	$44,816.89	5.1271%
Common savings account rates (US, 2024 reference)
High-Yield Savings	12	Typical APY: 4.5% - 5.3%			~5.0%
Traditional Savings	12	Typical APY: 0.01% - 0.5%			~0.25%
1-Year CD	12	Typical APY: 4.0% - 5.0%			~4.5%
5-Year CD	12	Typical APY: 3.5% - 4.5%			~4.0%
Money Market	12	Typical APY: 3.5% - 5.0%			~4.5%
Treasury I-Bonds	2	Rate adjusts semi-annually with CPI			~4.28% (2024)

Frequently Asked Questions

More frequent compounding means interest is calculated on previously earned interest sooner. Moving from annual to monthly compounding on a $10,000 deposit at 5% over 30 years adds approximately $1,458 to the final balance. The effect grows nonlinearly with both rate and time. Daily versus monthly adds far less ($139 over 30 years at 5%) because the marginal gain diminishes as n increases toward continuous compounding.

APR (Annual Percentage Rate) is the nominal stated rate - the variable r in the formula. APY (Annual Percentage Yield) accounts for intra-year compounding and represents the true annualized return. APY = (1 + r/n)^n − 1. A 5.00% APR compounded monthly yields an APY of 5.1162%. Banks are required by the Truth in Savings Act to disclose APY, so compare APY across accounts, not APR.

No. Interest earned in taxable savings accounts is subject to federal and potentially state income tax in the US. For a rough after-tax estimate, multiply the annual interest rate by (1 − marginal tax rate) before entering it. For example, at a 24% federal bracket, a 5% nominal rate becomes approximately 3.8% after tax. Tax-advantaged accounts (Roth IRA, 529) would use the full pre-tax rate.

This calculator assumes contributions align with compounding periods. If you contribute monthly but your account compounds daily, the result is an approximation. The discrepancy is small - typically under 0.1% of the final balance for rates below 10%. For exact modeling of mismatched frequencies, each contribution must be compounded individually from its deposit date, which requires day-count simulation.

At a 3% average inflation rate, $1 today has the purchasing power of roughly $0.41 in 30 years. To estimate real (inflation-adjusted) growth, subtract the expected inflation rate from your nominal rate. A 5% nominal rate with 3% inflation yields approximately 2% real growth. Over 30 years, $10,000 at 2% real growth reaches ~$18,114 in today's dollars versus the nominal $43,219.

This is the exponential nature of compounding. In early years, interest is earned primarily on the principal. As the balance grows, interest is earned on an increasingly larger base that includes prior interest. For a $10,000 deposit at 5% compounded monthly: Year 1 earns ~$512, Year 15 earns ~$1,065, and Year 30 earns ~$2,218. The interest-on-interest component dominates after approximately year 10-15 depending on the rate.