Essential Financial Formulas

A comprehensive reference guide to the most important financial formulas. Bookmark this page for quick access.

Quick Navigation:

Compound Interest•Loan Payment•ROI•NPV•IRR•Break-Even•Rule of 72

Compound Interest

A = P(1 + r/n)^nt

Variables:

A = Final amount
P = Principal (initial amount)
r = Annual interest rate (decimal)
n = Compounding frequency per year
t = Time in years

Example:

$10,000 at 5% annual interest, compounded monthly for 10 years:

A = 10,000(1 + 0.05/12)^12×10

= $16,470.09

Try our Compound Interest Calculator →

Loan Payment (Amortization)

M = P × [r(1+r)ⁿ] / [(1+r)ⁿ - 1]

Variables:

M = Monthly payment
P = Principal (loan amount)
r = Monthly interest rate (annual ÷ 12)
n = Total number of payments

Example:

$250,000 mortgage at 6% for 30 years:

r = 0.06/12 = 0.005, n = 360

M = $1,498.88/month

Try our Mortgage Calculator →

Return on Investment (ROI)

ROI = [(Final Value - Initial Investment) / Initial Investment] × 100

Simple ROI:

Measures the percentage gain or loss on an investment relative to its cost.

Example:

Invested $5,000, now worth $7,500:

ROI = [(7,500 - 5,000) / 5,000] × 100

= 50% return

Try our ROI Calculator →

Net Present Value (NPV)

NPV = Σ [C_t / (1+r)^t] - C₀

Variables:

C_t = Cash flow at time t
r = Discount rate
t = Time period
C₀ = Initial investment

Decision Rule:

NPV > 0: Investment adds value (accept)

NPV < 0: Investment destroys value (reject)

NPV = 0: Investment breaks even

Internal Rate of Return (IRR)

NPV = 0 = Σ [C_t / (1+IRR)^t] - C₀

Solve for IRR (usually requires iteration)

IRR is the discount rate that makes the NPV of all cash flows equal to zero. It represents the expected annual growth rate of an investment.

Decision Rule:

If IRR exceeds your required rate of return (hurdle rate), the investment is attractive.

Break-Even Analysis

Break-Even Units = Fixed Costs / (Price per Unit - Variable Cost per Unit)

Components:

Fixed Costs: Rent, salaries, insurance
Variable Costs: Materials, commission
Contribution Margin: Price - Variable Cost

Example:

Fixed costs: $50,000
Price: $100, Variable cost: $60

= $50,000 / ($100 - $60)

= 1,250 units to break even

Rule of 72

Years to Double = 72 / Interest Rate

A quick mental math shortcut to estimate how long it takes for an investment to double at a given interest rate.

Interest Rate	Years to Double
4%	18 years
6%	12 years
8%	9 years
10%	7.2 years
12%	6 years

Quick Reference Table

Formula	Use Case
Simple Interest = P × r × t	Short-term loans, treasury bills
Future Value = PV × (1 + r)ⁿ	Investment projections
Present Value = FV / (1 + r)ⁿ	Discounting future cash flows
Debt-to-Income = Monthly Debt / Monthly Income	Loan qualification
Profit Margin = (Revenue - Costs) / Revenue × 100	Business profitability

Essential Financial Formulas

Compound Interest

Variables:

Example:

Loan Payment (Amortization)

Variables:

Example:

Return on Investment (ROI)

Simple ROI:

Example:

Net Present Value (NPV)

Variables:

Decision Rule:

Internal Rate of Return (IRR)

Decision Rule:

Break-Even Analysis

Components:

Example:

Rule of 72

Quick Reference Table

Related Calculators