Displayed prefix, e.g., $, £, €.
Example Scenarios
| Mode | Parameters | Action |
|---|
Formulas Used
- Loan Payment (PMT):
PMT = r * PV / (1 - (1 + r)-n), whereris per-period rate,nperiods. - Amortization: Interestt = Balancet-1 * r; Principalt = PMT − Interestt; Balancet = Balancet-1 − Principalt.
- Future Value:
FV = PV (1+r)^n + PMT ((1+r)^n − 1)/r, payments at period end. - Present Value:
PV = FV / (1+r)^n(lump sum). Annuity:PV = PMT (1 − (1+r)^{-n})/r. - NPV:
NPV = \u2211 CF_t / (1+r)^tincluding initial outlay att=0. - IRR: rate where
NPV = 0; solved via Newton-Raphson with bisection fallback. - CAGR:
CAGR = (FV/PV)^{1/n} − 1. - ROI:
ROI = (Gain − Cost)/Cost. - Payback: periods until cumulative cash flow becomes non-negative.
- Straight-Line Depreciation:
Annual = (Cost − Salvage)/Life. - APR→EAR:
EAR = (1 + APR/m)^m − 1, m periods/year. - Growing Annuity PV:
PV = PMT_1 \u00D7 (1 - ((1+g)^n/(1+r)^n)) / (r-g). - Bond Price:
P = \u2211 \frac{C}{(1+y/f)^t} + \frac{F}{(1+y/f)^n}, coupons C=F\u00D7coupon/f.
How to Use This Calculator
- Pick a Mode matching your task.
- Provide inputs. Rates are annual; select compounding and timing.
- Click Calculate to see KPIs and detailed tables.
- Click Show/Update Chart to visualize the results.
- Use Add to Comparison to store scenario KPIs below.
- Download the current result as CSV or PDF.
Mode Cheatsheet: Inputs & Outputs
| Mode | Required Inputs | Key Outputs |
|---|---|---|
| Loan (PMT) | PV, APR, Years, Frequency, Timing | Per‑period payment, total interest, amortization schedule |
| Future Value | PV, PMT, APR, n, Frequency, Timing | FV, lump‑sum growth, annuity growth |
| Present Value | FV, PMT, APR, n, Frequency, Timing | PV, PV of lump sum, PV of annuity |
| NPV | Discount rate, CF₀, CF₁..CFₙ | NPV, discounted cash‑flow table |
| IRR | CF₀..CFₙ, initial guess | IRR %, NPV curve |
| CAGR | PV, FV, years | CAGR % and growth path |
| ROI | Cost, Gain | ROI %, net gain |
| Payback | CF₀, CF₁..CFₙ | Payback period, cumulative cash‑flow track |
| Depreciation (SL) | Cost, Salvage, Life | Annual expense, book value by year |
| APR ⇄ EAR | APR, compounding frequency | Effective annual rate |
| Balloon Loan | PV, APR, Term, Amort Years, Frequency | Payment, balloon amount, schedule |
| Growing Annuity | PMT₁, g, r, n, Timing | PV, FV, payment path |
| Bond Price | Face, coupon %, YTM %, years, freq | Clean price, price/yield curve |
| Bond YTM | Face, coupon %, price, years, freq | Yield to maturity %, price curve |
Practical Use Cases & Typical Values
| Scenario | Example Inputs | What to Monitor |
|---|---|---|
| Mortgage sizing | PV 25,000,000; APR 16%; 20 years; monthly | Payment affordability, total interest, balance tail |
| Retirement saving | PMT 25,000/month; APR 9%; 25 years | Future value, required PMT to reach target |
| Equipment purchase | Cost 4,000,000; Salvage 400,000; Life 5 | Annual depreciation vs projected income |
| Project appraisal | r 12%; CF₀ −10,000,000; CF 3, 3.5, 4, 4.5 | NPV sign, IRR vs hurdle rate, payback |
| Bond screening | Face 1,000; coupon 8%; price 1,050; 7 years | YTM vs benchmark, price/yield sensitivity |
Rate & Period Mapping (Quick Reference)
Use these to convert a nominal annual percentage rate into a per‑period rate for formulas.
| Frequency | m (periods/year) | Per‑period rate r | Example when APR = 12% |
|---|---|---|---|
| Annual | 1 | r = APR / 1 | 12.000% per year |
| Semiannual | 2 | r = APR / 2 | 6.000% per half‑year |
| Quarterly | 4 | r = APR / 4 | 3.000% per quarter |
| Monthly | 12 | r = APR / 12 | 1.000% per month |
| Daily | 365 | r = APR / 365 | ≈0.03288% per day |
Sensitivity Snapshot: Payment vs Rate & Term
Example loan sized at PV 1,000,000, monthly payments. Uses PMT = r·PV / (1 − (1+r)−n) with r = APR/12, n = years×12.
| APR (%) | Payment / Month |
|---|
| Term (years) | Payment / Month |
|---|
Tip: Adjust currency and decimals above; tables refresh on page load.
Prepayment Impact: Time & Interest Saved
Illustrative mortgage example with PV 1,000,000; APR 14%; 20 years; monthly. Extra payments reduce term and interest dramatically.
| Extra / Month | New Term (months) | Months Saved | Interest Saved |
|---|
Investment Growth Ladder: Monthly Contribution vs Future Value
FV with 9% annual return, monthly compounding, 20 years. Useful for retirement or education planning.
| Monthly Contribution | Years | Rate (%) | Future Value |
|---|
Glossary of KPIs
| KPI | Definition | Equation / Computation | Applies To |
|---|---|---|---|
| Payment (PMT) | Fixed periodic payment to amortize a loan. | PMT = r·PV / (1 − (1+r)−n) | Loan, Balloon |
| Future Value (FV) | Value of money after compounding and/or contributions. | FV = PV(1+r)^n + PMT\[(1+r)^n − 1\]/r | FV, CAGR, Growing Annuity |
| Present Value (PV) | Current worth of future amounts discounted at r. | PV = FV/(1+r)^n, annuity: PMT(1 − (1+r)^{-n})/r | PV, Bond |
| Net Present Value (NPV) | Discounted sum of project cash flows. | NPV = \sum CF_t/(1+r)^t | NPV, IRR |
| Internal Rate of Return (IRR) | Rate where NPV equals zero. | Solve \sum CF_t/(1+IRR)^t = 0 | IRR |
| Return on Investment (ROI) | Gain relative to cost. | (Gain − Cost)/Cost | ROI |
| CAGR | Smoothed average annual growth rate. | ((FV/PV)^{1/n} − 1) | CAGR |
| Payback Period | Time until cumulative cash flow becomes non‑negative. | Smallest t where \sum_{i=0}^t CF_i ≥ 0 | Payback |
| Depreciation Expense | Yearly allocation of asset cost. | (Cost − Salvage)/Life | Depreciation (SL) |
| Book Value | Carrying value after depreciation. | Cost − Accumulated Depreciation | Depreciation (SL) |
| Effective Annual Rate (EAR) | Annualized return accounting for compounding. | (1 + APR/m)^m − 1 | APR ⇄ EAR |
| Yield to Maturity (YTM) | Internal return of a bond’s cash flows at price. | Solve price = PV of coupons + principal | Bond YTM |
Data Validation & Error Hints
| Rule / Check | Why it matters | Hint |
|---|---|---|
| Amounts must be ≥ 0 | Negative PV, cost, or price can invalidate formulas. | Use negatives only for outflows in cash‑flow lists. |
| Rates usually between 0% and 200% | Extreme rates break discounting or convergence. | Enter percentages like 7.5, not 0.075. |
| Periods n must be > 0 | Payment, PV, FV require finite periods. | Set years × frequency to match reality. |
| IRR needs mixed signs | All‑positive or all‑negative flows have no root. | Include at least one negative and one positive. |
| Growing annuity r ≠ g | Division by zero when r equals g exactly. | If close, results remain well‑behaved numerically. |
| Bond inputs consistent | Coupon, price, maturity must align with frequency. | Pick annual/semi/quarterly and stick with it. |
| Timing choice matters | Begin vs end shifts discounting one period. | Use begin for rents, end for typical loans. |
| Decimals affect rounding | Exports and KPIs use your decimals setting. | Increase decimals for audit trails. |
- If a result looks odd, recheck percent inputs and frequency.
- CSV/PDF export mirrors on‑screen values with current decimals.
- NPV/IRR curves can be flat near roots; try a different range.
FAQs
Annual, semiannual, quarterly, monthly, and daily. Payment timing can be end or beginning of period for annuities.
It uses Newton-Raphson with derivative and a guarded bisection fallback on a wide bracket to improve robustness across varied cash flow shapes.
Yes. In Loan and Balloon Loan modes, full schedules are produced including principal, interest, and ending balance for each period.
Yes. Provide an initial cash flow at period zero (usually negative) and subsequent inflows/outflows for each period.
Periods correspond to the compounding/payment frequency selected. For example, monthly compounding means
n is in months.Use Add to Comparison to store key metrics in a table for quick side-by-side evaluation.
Click Download PDF. A built-in client library renders the results area as a PDF file instantly.
Scenario Comparison
| # | Mode | Primary Result | Secondary | Params |
|---|
Quick Tips
- APR should be entered as a percentage, e.g., 7.5.
- Choose compounding to match rate quoting (e.g., monthly mortgage).
- For IRR, include at least one negative and one positive flow.
- Use decimals setting to tailor rounding in reports/exports.
Disclaimer: For education and planning; verify before financial commitments.