Loan math: interest, LTV, points, amortization, and PITI

Keep the bases separate

Use the figures and conventions in the question; actual loan terms and escrow requirements vary.

Loan-to-value (LTV) = loan ÷ lender's value basis × 100%. For a purchase, that basis is commonly the lower of price and appraisal. A $240,000 loan on a $300,000 price and appraisal gives $240,000 ÷ $300,000 = 0.80 = 80% LTV. Down payment before costs = $300,000 − $240,000 = $60,000.

Simple interest = principal × annual rate × years. With an unchanged $240,000 balance at 6%, annual interest = $240,000 × 0.06 = $14,400; one month's interest = $14,400 ÷ 12 = $1,200. Use the stated time fraction for shorter periods.

Discount points are based on the loan, not the price. One point = 1% of the loan. Two points on $240,000 = $240,000 × 0.02 = $4,800. A point does not prescribe a one-percentage-point rate reduction. Simple break-even months = extra upfront cost ÷ monthly savings for the quoted alternatives.

Follow the balance

A standard fixed-rate, fully amortizing loan has level principal-and-interest payments. Interest uses the outstanding balance; the rest reduces principal. With an assumed first payment of $1,439 and $1,200 interest, principal paid = $1,439 − $1,200 = $239. New balance = $240,000 − $239 = $239,761. The next month's interest uses this smaller balance. Interest's share declines and principal's share grows. Interest-only payments leave principal unchanged; negative amortization adds unpaid interest to principal.

Build the housing payment

PITI means principal, interest, taxes, and insurance. Annual taxes of $3,600 ÷ 12 = $300 monthly. Annual property insurance of $1,200 ÷ 12 = $100 monthly. PITI = $1,439 + $300 + $100 = $1,839 monthly.

Mortgage insurance and association dues may be additional expenses. Fixed principal and interest do not freeze taxes or insurance, so the total payment can change.