Interest, Points & Loan Math
~12 min read · Compute simple interest, discount points, LTV and monthly principal-and-interest pieces.
Finance math loops three formulas: simple interest (principal × rate × time), the monthly-interest slice of an amortized payment, and the LTV/point calculations that price a loan. Every question is one of these wearing different clothes.
Interest mechanics
Simple interest: I = P × R × T (annual basis; divide by 12 for monthly). The amortization step the exam loves: first month's interest = balance × annual rate ÷ 12; principal reduction = payment − interest; next month recomputes on the smaller balance. Annual interest ÷ 12 also recovers a payment's interest share, and interest ÷ rate recovers the balance — T-bar logic again.
- I = PRT; monthly = balance × rate ÷ 12
- Payment − interest = principal reduction, month by month
- Balance = annual interest ÷ rate (reverse gear)
LTV, points, and PMI lines
LTV = loan ÷ lesser of price or appraised value; down payment = price − loan. Point = 1% of the LOAN; 'a loan at 90% LTV on a $400,000 price with 1.5 points' costs 400,000 × 0.9 × 0.015 = $5,400. PMI attaches above 80% LTV on conventional loans — the math question is usually 'how much down to avoid it': price-based unless the appraisal is lower.
- LTV off the lesser of price or value
- Points percentage rides the loan amount
- 80% LTV = the no-PMI down-payment target
Qualifying and payment ratios
Housing ratio = PITI ÷ gross monthly income; total ratio adds recurring debts. Reverse: max PITI = income × ratio limit. Amortization-factor problems supply a per-$1,000 payment factor: payment = (loan ÷ 1,000) × factor. Rent-multiplier and income problems (GRM, cap rate) round out the family — all T-bar variants.
Worked example
A $380,000 loan at 6% annual interest carries a $2,278 monthly P&I payment. Compute: (a) the first month's interest and principal reduction; (b) the balance after payment one; (c) the second month's interest. Then (d): the same buyer paid 2 points at closing on this loan — how much?
(a) First interest = 380,000 × 0.06 ÷ 12 = $1,900; principal reduction = 2,278 − 1,900 = $378. (b) New balance = 380,000 − 378 = $379,622. (c) Second interest = 379,622 × 0.06 ÷ 12 = $1,898.11 — a hair less, which is amortization's whole story: each payment shifts a little from interest to principal. (d) Points: 380,000 × 0.02 = $7,600. The exam's amortization questions rarely go past two or three months precisely because the method, not endurance, is the test: balance × rate ÷ 12, subtract, repeat.
Common exam pitfalls
Computing monthly interest on the original loan forever.
Each month's interest runs on the CURRENT balance — recompute after every principal reduction.
Taking points on the price.
Points are a percentage of the LOAN.
Using annual figures against monthly payments.
Divide annual interest by 12 before comparing to a monthly payment — mixed bases wreck the subtraction.
Balance times rate over twelve; payment minus interest shrinks the debt; points ride the loan.
Recap
- I = PRT; monthly interest = balance × rate ÷ 12
- Amortization: payment − interest = principal cut; recompute monthly
- Balance = annual interest ÷ rate
- LTV on the lesser of price/value; down payment fills the gap
- Point = 1% of loan amount
- Ratios and factors: T-bar arithmetic throughout
Prove it: 10 questions on this topic
Every lesson ends with a ten-question check in the free course — your progress syncs between the web and the EstatePass app.