Financial Math Formulas — Interest, Annuity & Loan Reference A complete reference of financial math formulas. Covers interest (simple, compound, continuous), annuities (ordinary and due), present and future value, loan and mortgage payments, depreciation, and return on investment.
Interest Formulas Simple Interest (Total Amount)
A = P ( 1 + r t ) A = P(1 + r t) A = P ( 1 + r t ) Compound Interest
A = P ( 1 + r n ) n t A = P\left(1 + \tfrac{r}{n}\right)^{n t} A = P ( 1 + n r ) n t A = P e r t A = P e^{r t} A = P e r t Effective Annual Rate
APY = ( 1 + r n ) n − 1 \text{APY} = \left(1 + \tfrac{r}{n}\right)^n - 1 APY = ( 1 + n r ) n − 1 Present Value & Future Value Future Value (Compound)
F V = P V ( 1 + r n ) n t FV = PV\left(1 + \tfrac{r}{n}\right)^{n t} F V = P V ( 1 + n r ) n t Present Value (Compound)
P V = F V ( 1 + r / n ) n t PV = \frac{FV}{(1 + r/n)^{n t}} P V = ( 1 + r / n ) n t F V Future Value (Continuous)
F V = P V ⋅ e r t FV = PV \cdot e^{r t} F V = P V ⋅ e r t Present Value (Continuous)
P V = F V ⋅ e − r t PV = FV \cdot e^{-r t} P V = F V ⋅ e − r t Rule of 72 (Doubling Time)
t × 2 ≈ 72 r % t_{\times 2} \approx \frac{72}{r\%} t × 2 ≈ r % 72 Annuities Future Value (Ordinary Annuity)
F V = P M T ⋅ ( 1 + i ) n − 1 i FV = PMT \cdot \frac{(1 + i)^n - 1}{i} F V = P M T ⋅ i ( 1 + i ) n − 1 Present Value (Ordinary Annuity)
P V = P M T ⋅ 1 − ( 1 + i ) − n i PV = PMT \cdot \frac{1 - (1 + i)^{-n}}{i} P V = P M T ⋅ i 1 − ( 1 + i ) − n Future Value (Annuity Due)
F V = P M T ⋅ ( 1 + i ) n − 1 i ( 1 + i ) FV = PMT \cdot \frac{(1 + i)^n - 1}{i}(1 + i) F V = P M T ⋅ i ( 1 + i ) n − 1 ( 1 + i ) Present Value (Annuity Due)
P V = P M T ⋅ 1 − ( 1 + i ) − n i ( 1 + i ) PV = PMT \cdot \frac{1 - (1 + i)^{-n}}{i}(1 + i) P V = P M T ⋅ i 1 − ( 1 + i ) − n ( 1 + i ) Perpetuity (PV)
P V = P M T i PV = \frac{PMT}{i} P V = i P M T Loans & Mortgages Monthly Payment
P M T = P ⋅ i ( 1 + i ) n ( 1 + i ) n − 1 PMT = \frac{P \cdot i (1 + i)^n}{(1 + i)^n - 1} P M T = ( 1 + i ) n − 1 P ⋅ i ( 1 + i ) n Total Paid Over Life of Loan
T = P M T ⋅ n T = PMT \cdot n T = P M T ⋅ n Loan Balance After k Payments
B k = P ( 1 + i ) k − P M T ⋅ ( 1 + i ) k − 1 i B_k = P(1+i)^k - PMT \cdot \tfrac{(1+i)^k - 1}{i} B k = P ( 1 + i ) k − P M T ⋅ i ( 1 + i ) k − 1 Depreciation Straight-Line Depreciation
D = C − S n D = \frac{C - S}{n} D = n C − S Declining Balance
V t = C ( 1 − r ) t V_t = C(1 - r)^t V t = C ( 1 − r ) t Book Value After t Years
B V t = C − D ⋅ t BV_t = C - D \cdot t B V t = C − D ⋅ t Return on Investment & Growth Return on Investment (ROI)
ROI = Gain − Cost Cost × 100 % \text{ROI} = \frac{\text{Gain} - \text{Cost}}{\text{Cost}} \times 100\% ROI = Cost Gain − Cost × 100% Compound Annual Growth Rate (CAGR)
CAGR = ( F V P V ) 1 / n − 1 \text{CAGR} = \left(\frac{FV}{PV}\right)^{1/n} - 1 CAGR = ( P V F V ) 1/ n − 1 Profit Margin
Margin = Profit Revenue × 100 % \text{Margin} = \frac{\text{Profit}}{\text{Revenue}} \times 100\% Margin = Revenue Profit × 100% Markup
Markup % = Selling Price − Cost Cost × 100 % \text{Markup}\% = \frac{\text{Selling Price} - \text{Cost}}{\text{Cost}} \times 100\% Markup % = Cost Selling Price − Cost × 100% 