Finance & Interest

Interest, loans, investments and valuation

The Finance & Interest category brings together the key formulas used to understand interest, loans, investments, and valuation, from simple and compound interest to present value, future value, EMI, CAGR, and net present value. It’s useful for students, exam preparation, and real-world decision-making, helping you compare borrowing costs, estimate returns, and make smarter financial choices with confidence.

Simple Interest

I = P r t

Interest earned on principal at a simple rate.

Compound Interest

A = P\left(1 + \frac{r}{n}\right)^{nt}

Value of principal compounded n times per year.

Continuous Compounding

A = P e^{rt}

Value with interest compounded continuously.

Future Value

FV = PV(1 + r)^n

Future worth of a present sum.

Present Value

PV = \frac{FV}{(1 + r)^n}

Present worth of a future sum.

Future Value of Annuity

FV = P\frac{(1+r)^n - 1}{r}

Future value of regular equal payments.

Present Value of Annuity

PV = P\frac{1 - (1+r)^{-n}}{r}

Present value of a series of equal payments.

Loan EMI

EMI = \frac{P r (1+r)^n}{(1+r)^n - 1}

Equated monthly installment on a loan.

CAGR

CAGR = \left(\frac{V_f}{V_i}\right)^{1/n} - 1

Compound annual growth rate of an investment.

Return on Investment

ROI = \frac{V_f - V_i}{V_i} \times 100\%

Percentage gain or loss on an investment.

Rule of 72

t \approx \frac{72}{r}

Approximate years to double an investment.

Net Present Value

NPV = \sum_{t=0}^{n}\frac{C_t}{(1+r)^t}

Present value of a stream of cash flows.

Perpetuity

PV = \frac{C}{r}

Present value of an infinite constant cash flow.

Straight-Line Depreciation

D = \frac{C - S}{n}

Annual depreciation of an asset.

Effective Annual Rate

EAR = \left(1 + \frac{r}{n}\right)^n - 1

True annual rate accounting for compounding.

Break-Even Point

Q = \frac{FC}{P - VC}

Units to sell to cover all costs.

Profit

\text{Profit} = \text{Revenue} - \text{Cost}

The money left after subtracting cost from revenue.

Profit Margin

\text{Margin} = \frac{\text{Profit}}{\text{Revenue}} \times 100\%

Profit as a percentage of revenue.

Markup

\text{Markup} = \frac{\text{Price} - \text{Cost}}{\text{Cost}} \times 100\%

Increase over cost as a percentage.

Price-to-Earnings Ratio

PE = \frac{\text{Price}}{\text{EPS}}

Share price relative to earnings per share.

Earnings Per Share

EPS = \frac{\text{Net Income}}{\text{Shares}}

Company profit allocated to each share.

Dividend Yield

Y = \frac{\text{Dividend}}{\text{Price}}\times 100

Annual dividend as a percentage of share price.

Break-Even Point

Q = \frac{FC}{P - VC}

Units to sell to cover all costs.

Gross Margin

GM = \frac{Revenue - COGS}{Revenue}\times 100

Percentage of revenue left after cost of goods.

Current Ratio

CR = \frac{\text{Current Assets}}{\text{Current Liabilities}}

Liquidity measure of short-term solvency.

Debt-to-Equity Ratio

D/E = \frac{\text{Total Debt}}{\text{Equity}}

Leverage measure comparing debt to equity.

Return on Equity

ROE = \frac{\text{Net Income}}{\text{Equity}}\times 100

Profit generated per dollar of equity.

Return on Assets

ROA = \frac{\text{Net Income}}{\text{Total Assets}}\times 100

Profit generated per dollar of assets.

Real Rate of Return

r = \frac{1+n}{1+i} - 1

Return adjusted for inflation.

Payback Period

PP = \frac{\text{Initial Investment}}{\text{Annual Cash Flow}}

Time to recover an investment.

Working Capital

WC = \text{Current Assets} - \text{Current Liabilities}

Short-term financial health of a business.

Black-Scholes (Call Option)

C = S_0\,N(d_1) - K e^{-rT} N(d_2)

Prices a European call option, where d₁ and d₂ depend on the stock price, strike, volatility, rate and time. N(·) is the standard normal CDF.