How repeated compounding turns one deposit into a future balance
Compound interest adds each period's interest to the balance, allowing later interest to accrue on earlier interest. It helps compare the effect of term and compounding frequency.
The growth chart plots sampled year-end balances calculated with the selected frequency. It includes year zero, so the starting point and final balance can be compared directly.
A year-end growth chart connects the starting principal to the final balance. The interest-earned figure is shown separately, so modeled growth is not confused with the money originally entered.
How starting amount, rate, years and compounding frequency interact
Only four inputs drive this result, and they do not carry equal weight. The rate and the years sit in the exponent, while the starting amount simply scales the answer.
- Starting amount
- The single deposit that compounds for the whole term; nothing is added or withdrawn later. The result scales in exact proportion, so doubling 1,000 to 2,000 doubles both the balance and the interest. Planned monthly top-ups cannot be entered here, and leaving them out understates the balance; the Investment Calculator handles regular deposits.
- Annual interest rate
- A nominal yearly percentage that the tool divides by the compounding frequency. Because it sits inside the exponent, its effect grows with time: over 2 years with monthly compounding, 5% earns 104.94 on 1,000 while 10% earns 220.39, more than double. Type 5 for five percent; 0.05 is read as one twentieth of one percent.
- Time in whole years
- How long the balance compounds, from 1 to 100 whole years. Over long periods time outweighs everything else: 1,000 at 5% compounded monthly grows to 1,104.94 after 2 years but 2,712.64 after 20, lifting interest from 104.94 to 1,712.64. A 30-month term cannot be entered directly.
- Compounding frequency
- How many times a year interest is added to the balance: annually, quarterly, monthly or daily. More frequent compounding helps only slightly at ordinary rates: 1,000 at 5% for 2 years reaches 1,102.50 annually, 1,104.94 monthly and 1,105.16 daily. Pick the frequency stated in the account terms rather than the most frequent option.
Steps
- Enter the starting amount and fixed annual rate.
- Enter a whole number of years and choose how often interest compounds.
- Calculate to see future balance and interest earned in the same currency units.
Reading tip: Compare the chart's first and last points with the displayed interest-earned fact. Expand the plotted-values list for the sampled balances used to draw the curve.
Questions a lump-sum compounding projection can settle
Savings goals
Estimate a future balance for a fixed principal and rate.
Frequency comparisons
Compare annual, quarterly and monthly compounding assumptions.
Long-term planning
See how additional years change modeled growth.
Interest breakdown
Separate the starting amount from calculated interest earned.
How the calculation works
- A
- Future balance after all selected compounding periods.
- P
- Starting principal; no later deposits are assumed.
- r
- Fixed nominal annual interest rate entered as a percentage.
- n / t
- Compounding periods per year / whole number of years.
The curve shows selected year-end balances from the same formula; it assumes the rate never changes.
What every part means
- A
- Future balance after all selected compounding periods.
- P
- Starting principal; no later deposits are assumed.
- r
- Fixed nominal annual interest rate entered as a percentage.
- n / t
- Compounding periods per year / whole number of years.
Calculate it step by step
The nominal annual rate is spread evenly over the selected periods.
Each completed period compounds the balance once.
This model has no later deposits or withdrawals.
Decimal arithmetic preserves intermediate precision. At each chart sample, the same compound-growth formula is evaluated at a whole-year point; at most eleven points keep long terms readable.
See how Calculation Guide tests examples and handles calculation limits.
See it in practice
- Starting amount
- 1000 currency units
- Annual interest rate
- 5 %
- Time
- 2 whole years
- Compound interest
- Monthly
P = 1,000, r = 5%, n = 12, t = 2: A = 1,000 × (1 + 5/1,200)^24 ≈ 1,104.94; interest ≈ 104.94.
- Interest earned104.94
- Starting amount1,000
Interpretation & limitations
How to read your result
The gap between the final balance and principal is modeled interest. A higher frequency can increase the balance slightly at the same nominal annual rate; the graph does not represent a forecast of variable market returns.
Where this estimate stops
The rate stays fixed, and no contributions, withdrawals, taxes or fees are modeled. If your product compounds on a different schedule or calculates interest on daily balances, actual figures can differ.
Frequently asked questions
01Does a zero interest rate work?
Yes. The future balance remains the starting amount.
02Are deposits during the term included?
No. This version compounds only the starting amount.
03Why does the curve bend upward?
Each period's interest becomes part of the balance that earns interest in later periods.
04Is the displayed annual rate an effective annual rate?
No. The input is treated as a nominal annual rate divided evenly by the selected number of periods.
05Can I model monthly contributions?
No. This version grows only the initial principal. Additional deposits need a separate cash-flow model.
06Why are only some years listed for long terms?
The graph samples at most eleven points for clarity while the final result still applies every compounding period.
07My account advertises an APY. Which compounding frequency should I choose?
An APY already includes the effect of compounding, so choose Annual to avoid compounding it twice. For 1,000 over 2 years, a 5% APY entered as annual gives 1,102.50; the same 5% entered with monthly compounding gives 1,104.94, which overstates growth. Use a more frequent option only when the quoted figure is a nominal rate.
08Can this show the effective annual rate of a nominal rate?
Yes, with a one-year run. Enter 1,000 for 1 year at the nominal rate and its compounding frequency, then divide interest earned by 1,000. At 5% compounded monthly, interest is 51.16, an effective annual rate of about 5.116%.
Sources & references
Articles that use this calculator
- Extra Principal Payments: How Much Interest and Time You SaveOn a 300,000, 30-year loan at 6.75%, adding 100 a month to principal saves about 65,000 in interest and ends the loan 49 months early. Savings rise with every extra amount, but each additional unit buys fewer months than the one before.
- Compound vs Simple Interest: Worked Examples Over 30 YearsSimple interest pays the same amount every year on the original principal; compound interest pays on a growing balance. At 8%, the two match in year one, differ by 3,589.25 after 10 years and by 66,626.57 after 30 years on a 10,000 deposit.
- Nominal Rate vs Effective Annual Rate: How Compounding Changes ItThe effective annual rate is (1 + r ÷ n)^n − 1. A 12% nominal rate is 12% effective with annual compounding, 12.55% quarterly, 12.68% monthly and 12.75% daily, and the gap grows quickly at higher rates.