Finance Formulas — Complete Reference Sheet

P = principal, r = annual rate (decimal), t = time (years)

Interest earned or paid on the original principal only — no compounding.

n = compounding periods per year, t = years

Grows principal with interest added periodically to the accumulated balance.

e ≈ 2.71828 (Euler's number)

Theoretical upper bound of compounding — interest is added at every instant.

r = nominal annual rate, n = compounding periods per year

The effective annual return accounting for intra-year compounding.

P = loan amount, r = monthly rate, n = total monthly payments

Fixed monthly payment for a fully amortizing loan (mortgage, auto, personal).

M = monthly payment, n = number of payments, P = principal

The total cost of borrowing over the full loan term.

k = number of payments made so far

Outstanding balance after k payments have been made.

Result expressed as a percentage

Key metric used by lenders; LTV above 80% typically requires PMI.

Gain = final value of investment, Cost = initial cost

Percentage return relative to the original cost of the investment.

PV = present value, r = rate per period, n = periods

Projects how much a current sum will be worth at a future date.

FV = future value, r = discount rate per period

Today's value of a future sum of money, discounted for the time value of money.

r = annual interest rate as a percentage (e.g., 6 for 6%)

Quick mental estimate of how long it takes an investment to double in value.

CFₜ = cash flow in period t, r = discount rate

Sum of discounted future cash flows minus the upfront investment — positive NPV means profitable.

EV = ending value, BV = beginning value, n = years

Smoothed annual growth rate over multiple years, as if growth were constant each year.

NOI = Net Operating Income (annual)

Core metric for comparing investment properties; higher cap rate = higher yield (and typically more risk).

Result expressed as a percentage

Lenders typically require DTI below 43% for mortgage approval.

Quick valuation shortcut; lower GRM indicates a potentially better deal.

Annual return on the actual cash you invested, before taxes.

COGS = Cost of Goods Sold

Percentage of revenue retained after direct production costs.

Price = selling price per unit

Number of units that must be sold to cover all costs with zero profit or loss.

Percentage added to cost to arrive at the selling price.

Profit allocated to each outstanding share; key metric for stock valuation.

EPS = Earnings Per Share

How much investors pay for each dollar of earnings; high P/E can signal growth expectations.