Real Estate & Mortgages

Property maths: mortgage payments, LTV, cap rate, rental yield, ROI and price per area

Real estate and mortgage formulas help you work out the numbers behind buying, owning, renting, and financing property. From EMI and loan-to-value ratio to rental yield, cap rate, and affordability checks, this category is useful for students, exam prep, and professionals handling property analysis, mortgages, or investment decisions. These formulas make it easier to compare deals, estimate returns, and avoid costly mistakes.

Mortgage Monthly Payment (EMI)

NEWIntermediate

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

Fixed monthly repayment on a mortgage.

Loan-to-Value Ratio

LTV = \frac{L}{V} \times 100

Loan size as a percentage of property value.

Capitalisation Rate

NEWIntermediate

CR = \frac{NOI}{V} \times 100

Annual return on a property from net operating income.

Gross Rental Yield

Y = \frac{12 R}{V} \times 100

Annual rent as a percentage of property price.

Net Operating Income

NOI = GI - OE

Rental income minus operating expenses.

Price per Square Metre

p = \frac{V}{A}

Property price divided by floor area.

Return on Investment

ROI = \frac{Gain}{Cost} \times 100

Profit as a percentage of money invested.

Cash-on-Cash Return

NEWIntermediate

CoC = \frac{ACF}{I_{cash}} \times 100

Annual cash flow relative to actual cash invested.

Debt Service Coverage Ratio

NEWIntermediate

DSCR = \frac{NOI}{D}

Whether rental income covers the loan payments.

Affordability (28% Rule)

M_{max} = 0.28 \times I

Recommended maximum housing payment from gross income.

Total Mortgage Interest

NEWIntermediate

I = (M \times n) - P

Total interest paid over the life of a loan.

Property Appreciation

V_n = V_0 (1 + g)^n

Future value from an annual appreciation rate.

After-Repair Value Rule (70%)

O_{max} = 0.7\, ARV - C_r

Max purchase price for a flip using the 70% rule.

Break-Even Occupancy

BE = \frac{OE + D}{GPI}

Occupancy needed to cover expenses and debt.