👤
Susovon Jana, Ph.D.
📖 Documentation · Academic Edition v2.0

Universal Financial
Calculator Guide

A comprehensive interactive reference covering every formula, parameter, and worked example across all FinCalc Pro modules.

9
Categories
40+
Tools
30+
Formulas
100%
Interactive
💡
Core Financial Concepts
Foundational theory underlying every module in FinCalc Pro

Time Value of Money (TVM)

The cornerstone of all financial mathematics: a rupee today is worth more than a rupee tomorrow because money available now can be invested to earn a return. Every present-value and future-value computation in FinCalc Pro derives from this single axiom.

FV = PV × (1 + r)ⁿ   |   PV = FV / (1 + r)ⁿ
r = interest / discount rate per compounding period (enter as decimal)
n = total number of compounding periods (not years, unless compounding is annual)
More frequent compounding → higher effective yield for the same nominal rate
Rule of 72: doubling time ≈ 72 / (rate in %)

Discounting & Net Present Value

To compare cash flows at different points in time, we bring all amounts to a common reference — usually today — using a discount rate reflecting risk and opportunity cost. The NPV of a project is the sum of all discounted cash flows including the initial outlay.

NPV = Σₜ₌₀ⁿ CFₜ / (1+r)ᵗ   |   Accept if NPV ≥ 0

A higher discount rate assigns less value to distant cash flows, making long-duration projects more sensitive to rate changes — exactly what bond duration measures.

Risk, Return & Diversification

Higher expected returns always come with higher risk. FinCalc Pro quantifies this trade-off using variance and standard deviation as measures of total risk, and correlation to measure co-movement between assets.

E(R) = Σ pᵢ × Rᵢ   |   σ² = Σ pᵢ(Rᵢ − E(R))²   |   ρ = Cov/(σ₁σ₂)
Portfolio variance depends on correlation: lower ρ → greater diversification benefit
CAPM prices only systematic (market) risk via Beta; idiosyncratic risk is diversifiable
Efficient Frontier: the set of portfolios offering the highest return for a given risk level
Sharpe Ratio measures excess return per unit of total risk (σₚ)

Bond Pricing & Interest Rate Sensitivity

A bond's fair price equals the present value of all future coupon payments plus the face value, discounted at the yield to maturity (YTM). Price and yield move inversely.

P = Σ C/(1+y)ᵗ + FV/(1+y)ⁿ   |   Modified Duration ≈ −ΔP/P per Δy
Coupon Rate < YTM → bond trades at a discount (price < face value)
Macaulay Duration = weighted average time to receive cash flows
Convexity corrects duration's linear approximation — beneficial for bondholders

Derivatives & Option Greeks

The Black-Scholes-Merton (BSM) model prices European options under assumptions of log-normal asset prices, constant volatility, and continuous trading. The five Greeks measure sensitivities of option value to underlying parameters.

C = S·N(d₁) − K·e^(−rT)·N(d₂)   |   d₁ = [ln(S/K) + (r + σ²/2)T] / (σ√T)
Delta (Δ): change in option price per ₹1 move in underlying — the hedge ratio
Gamma (Γ): rate of change of delta — measures convexity of option position
Theta (Θ): daily time decay — at-the-money options decay fastest near expiry
Vega: sensitivity to 1% change in implied volatility
Rho (ρ): sensitivity to 1% change in risk-free rate
📋
Formula Quick Reference
All key formulas across FinCalc Pro — hover rows to highlight
Formula NameMathematical ExpressionModule
Future ValueFV = PV × (1+r)ⁿTVM, FD
Present ValuePV = FV / (1+r)ⁿTVM, Bonds, NPV
Implied Rater = (FV/PV)^(1/n) − 1TVM, Returns
Periods Requiredn = ln(FV/PV) / ln(1+r)TVM
FV Annuity (ordinary)FVA = PMT × [(1+r)ⁿ − 1] / rTVM, RD
PV Annuity (ordinary)PVA = PMT × [1 − (1+r)⁻ⁿ] / rTVM, Loans
PerpetuityPV = PMT / rTVM
Growing PerpetuityPV = PMT / (r − g), requires r > gTVM, DDM
EMI (Reducing Balance)EMI = P × r × (1+r)ⁿ / [(1+r)ⁿ − 1]Banking
FD Maturity (Cumulative)A = P × (1 + r/q)^(q×t)Banking
RD MaturityM = Σ R × (1 + r_q)^(quarters remaining)Banking
Bond PriceP = Σ C/(1+y)ᵗ + FV/(1+y)ⁿBonds
Macaulay DurationD = Σ [t × PV(CFₜ)] / PBonds
Modified DurationMD = D / (1 + y)Bonds
ConvexityConv = Σ [t(t+1) × CF / (1+y)^(t+2)] / PBonds
Expected ReturnE(R) = Σ pᵢ × RᵢRisk & Return
Varianceσ² = Σ pᵢ × (Rᵢ − E(R))²Risk & Return
CovarianceCov = Σ pᵢ × (R₁ᵢ − Ē₁)(R₂ᵢ − Ē₂)Risk & Return
Correlationρ₁₂ = Cov(R₁,R₂) / (σ₁ × σ₂)Risk, Portfolio
Portfolio ReturnE(Rₚ) = w₁R₁ + w₂R₂Portfolio
Portfolio Varianceσₚ² = w₁²σ₁² + w₂²σ₂² + 2w₁w₂Cov₁₂Portfolio
CAPME(Rᵢ) = Rƒ + βᵢ × (E(Rₘ) − Rƒ)Portfolio
Futures P&L (Long)P&L = Sₜ − F₀Derivatives
Option Intrinsic (Call)max(Sₜ − K, 0)Derivatives
Black-Scholes CallC = S·N(d₁) − K·e^(−rT)·N(d₂)Derivatives
Black-Scholes PutP = K·e^(−rT)·N(−d₂) − S·N(−d₁)Derivatives
Delta (Call)Δ = N(d₁)Derivatives
GammaΓ = φ(d₁) / (S × σ × √T)Derivatives
NPVNPV = Σ CFₜ / (1+r)ᵗ, t=0 to nCorporate Finance
IRR0 = Σ CFₜ / (1+IRR)ᵗ [bisection]Corporate Finance
WACC(E/V)×Rₑ + (D/V)×Rᵈ×(1−Tᶜ)Corporate Finance
ROE / ROANI/Equity  |  NI/AssetsRatios
Current / Quick RatioCA/CL  |  (CA−Inv)/CLRatios
P/E & P/B RatioPrice/EPS  |  Price/(Book/Share)Ratios
Simple ReturnR = (P₁ − P₀ + D) / P₀Market Tools
Log Returnr = ln(P₁ / P₀)Market Tools
Annualized Volatilityσ_ann = σ_periodic × √freqMarket Tools
Sharpe Ratio(Rₚ − Rƒ) / σₚMarket Tools