§ Tools / Series 03 · Personal finance
Compound interest calculator
The textbook FV = P × (1 + r/n)^(n × t) formula, made into a real planning tool — with optional recurring contributions, independent unit scaling for the lump sum and the recurring amount, fee / inflation / tax drag, and a head-to-head comparison of how each compounding frequency changes the same plan.
§ Mixed-frequency correctness
Compounding frequency and contribution frequency can differ. Daily compounding with monthly deposits? Yearly compounding with weekly deposits? The math normalizes through an effective annual yield, then converts to a contribution-period rate — the trace shows both. Most simple calculators conflate the two.
3
Presets
5×5
Compounding × contrib
7
Rate scenarios
Per-period
Yearly schedule
v1
Methodology
§ Start with a preset
Three product-neutral starting points — adjust anything after.
Inputs
Independent units for lump sum and recurring deposit · everything recomputes instantly.
Future value · gross
$775.77
Over 5 years at 12% monthly compounding with $5.00 monthly deposits. You invested $500.00.
Interest earned$276
Growth multiple1.55×
Initial principal
$200
200 × ones
Total contributions
$300
60 × monthly
Absolute return
55.15%
interest / total invested
Effective annual yield
12.683%
vs typed 12% nominal
Net yield · after fees
12.683%
no fee modeled
Per-period rate · contributions
1.0000%
per monthly
§ Initial vs recurring
How much of the final corpus came from each leg?
Initial · 46.8% Recurring · 53.2%
§ Compounding comparison
How much does compounding frequency actually change your future value?
| Compounding | Periods / yr | Effective yield | Net yield | Future value | vs yearly |
|---|---|---|---|---|---|
| Yearly | 1 | 12.0000% | 12.0000% | $757.99 | — |
| Half-yearly | 2 | 12.3600% | 12.3600% | $767.32 | +$9.33 |
| Quarterly | 4 | 12.5509% | 12.5509% | $772.31 | +$14.33 |
| Monthly selected | 12 | 12.6825% | 12.6825% | $775.77 | +$17.78 |
| Daily | 365 | 12.7475% | 12.7475% | $777.48 | +$19.50 |
§ Contribution lever
What if you raised — or stopped — the recurring deposit?
No recurring
$0.0 / monthly
$363
invested $200
Current
$5.00 / monthly
$776
invested $500
2× current
$10.0 / monthly
$1,188
invested $800
§ Rate scenarios
What if the assumed rate moves by 25 / 50 / 100 bps?
-100 bps
11.00%
$747
FV
-50 bps
11.50%
$761
FV
-25 bps
11.75%
$768
FV
Base
12.00%
$776
FV
+25 bps
12.25%
$783
FV
+50 bps
12.50%
$791
FV
+100 bps
13.00%
$806
FV
§ Year-by-year schedule
The path, not just the endpoint
| Year | Opening | Contributions | Interest | Closing | Cumulative invested | Cumulative interest |
|---|---|---|---|---|---|---|
| Y1 | $200.00 | +$60.00 | +$29.41 | $289.41 | $260 | $29.4 |
| Y2 | $289.41 | +$60.00 | +$40.75 | $390.16 | $320 | $70.2 |
| Y3 | $390.16 | +$60.00 | +$53.53 | $503.69 | $380 | $124 |
| Y4 | $503.69 | +$60.00 | +$67.93 | $631.62 | $440 | $192 |
| Y5 | $631.62 | +$60.00 | +$84.15 | $775.77 | $500 | $276 |
§ Formula trace
- initialPrincipal = 200 × ones = 200.00 USD
- regularContribution = 5 × ones = 5.00 / monthly
- effectiveAnnualYield = (1 + 12% / 12)^12 − 1 = 12.6825%
- initialFutureValue = 200.00 × (1 + netYield)^5 = 363.34
- contributionPeriodRate = (1 + netYield)^(1/12) − 1 = 1.000000%
- recurringFutureValue = annuity(5.00, 1.0000%, 60, beginning) = 412.43
- totalInvested = 200.00 + 5.00 × 60 = 500.00
- futureValueGross = initialFV + recurringFV = 775.77
- grossInterestEarned = FV − totalInvested = 275.77
§ Input audit
annualRatePctused
compoundingused
currencyused
feeRatePctdefaulted
inflationPctdefaulted
initialAmountused
initialUnitused
rateConventionused
regularAmountused
regularFreqused
regularUnitused
taxRatePctdefaulted
tenureYearsused
timingused
§ Warnings
- Returns are assumptions, not guarantees. Taxes, fees, and inflation vary by product, jurisdiction, and time.
§ Golden references · locked in tests
Reference case: initial $200 + $5/month, 12%, 5 years, monthly compounding, beginning-of-period.
Initial FV
$363.34
Recurring FV
$412.43
Future value
$775.77
Interest earned
$275.77
Effective yield
12.6825%
Compounding fixture: $1,000 + $100/month, 8%, 10 years, beginning-of-period — same plan at four frequencies. The ~$381 spread is the cost of slower compounding.
Yearly
$20,287.24
Quarterly
$20,569.71
Monthly
$20,636.21
Daily
$20,668.88
§ Specialized siblings
§ Same engine, headlessly
Mixed-frequency math, fee drag, inflation deflator, contribution comparison, rate scenarios, and the yearly schedule are all reachable as a stateless REST endpoint and an MCP tool. Workbook CRUD is authenticated and stored under calculator_id=compound_interest.
POST/api/v1/financial-calculators/compound-interest/calculate
POST/api/v1/financial-calculators/compound-interest/run
GET/api/v1/financial-calculators/compound-interest/schema
GET/api/v1/financial-calculators/compound-interest/defaults
GET/api/v1/user/financial-calculator-workbooks?calculator_id=compound_interest · individual+
MCP tool
calculate_compound_interestmethodology_version = financial-calculators.v1 · canonical = /en/tools/compound-interest-calculator
§ FAQ
Four things worth knowing
Q01Why does the effective annual yield differ from the rate I typed?+
Compounded rates and quoted rates are different things. A 12% APR compounded monthly produces an effective annual yield of about 12.6825% — that extra 0.68% is interest-on-interest within the year. Toggle Rate convention → Effective annual to treat your input as the already-compounded yield instead. The Compounding comparison table makes the gap explicit across yearly / half-yearly / quarterly / monthly / daily.
Q02My compounding frequency differs from my contribution frequency. Does the math still work?+
Yes — that's the calculator's main job. Most simple compound-interest tools pretend the two are the same. Here we normalize first to an effective annual yield, then convert that yield to a contribution-period rate. So daily-compounding savings with monthly SIP-style deposits computes correctly. The contribution-period rate appears in the formula trace.
Q03Beginning of period or end of period — does it matter?+
Over decades, yes. Beginning-of-period (annuity due) means each contribution earns interest for one extra period. End-of-period (ordinary annuity) means the last contribution earns nothing. The gap can be a percent or two of final corpus — worth getting right rather than burying.
Q04How is the 'real' future value computed?+
realFV = futureValueGross / (1 + inflation rate)^tenure. It is the gross nominal future value deflated by inflation over the same horizon — what your projection buys in today's purchasing power. Tax and inflation are separate adjustments so you can mix and match.