30-Year Fixed vs ARM: Which Mortgage Is Better? A 7/6 ARM Case: the short version

New on FinoLib · Volume V: Personal Finance

I have just published a new article on FinoLib, my free finance education library: 30-Year Fixed vs ARM: Which Mortgage Is Better? A 7/6 ARM Case. It is part of Volume V: Personal Finance. It is part 3 of a 4-part guide. Below is a summary of the topic in plain, expert language, so you can follow the idea even before you open the full article.

A closer look

Why the early years are mostly interest. Each month’s interest is simply the outstanding balance × the monthly rate; whatever is left of the fixed payment repays principal. In month one of the 30-year loan above, interest is $300,000 × 0.5667% = $1,700.00, so only $1,955.78 − $1,700.00 = $255.78 reduces the balance. Because the balance falls slowly at first, interest stays high; as it falls, each payment’s interest share shrinks and its principal share grows, which in turn shrinks the balance faster. Year 1 sends $20,303 of $23,469 in payments to interest (86.5%); year 20 splits almost evenly. On this loan the principal part of a payment first exceeds the interest part at payment 239 — almost 20 years in — and half the original balance is not repaid until year 22.

Three line items on a Loan Estimate routinely confuse first-time buyers, and all three affect the real monthly and lifetime cost of a mortgage well beyond the headline interest rate.

A worked example

Worked Example — 30-Year vs 15-Year, Same $300,000 Loan

At illustrative rates of 6.8% for a 30-year fixed and 6.1% for a 15-year fixed, a $300,000 loan costs $1,955.78/month and $404,079 in total interest over 30 years, versus $2,547.81/month and just $158,605 in total interest over 15 years. The shorter term costs $592.03 more per month but saves $245,474 in lifetime interest — the same trade-off Part 3.3 showed between a credit card’s minimum payment and a fixed payment above it, at a much larger scale. The payment formula: payment = loan × i ÷ (1 − (1 + i)^−n), where i is the monthly rate and n the number of payments.

Analogy

Think of the outstanding balance as the part of the house the lender still owns, and interest as the rent you pay it for that share. Each payment covers this month’s rent first; whatever is left buys back a slice of the lender’s share. At the start the lender’s share is large, so most of the payment is rent and the slice is thin.

More from the article

■Discount points: a one-time upfront fee — one point equals 1% of the loan amount — paid to permanently lower the interest rate, often by roughly 0.25 percentage point per point (pricing varies by lender and by day).

■Private Mortgage Insurance (PMI): required on most conventional loans with less than 20% down, typically costing about $30–$70 a month per $100,000 borrowed (roughly 0.36%–0.84% a year, more with lower credit scores or smaller down payments), paid monthly, protecting the lender — not the borrower…

■Escrow: a lender-held account, funded through the monthly mortgage payment, that collects and pays property taxes and homeowners insurance on the borrower’s behalf — convenient, but it also means a jump in either bill shows up as a payment increase the following year, not as…

■Monthly payment after year 7 — $2,052.64 — $1,897.86

About FinoLib: it is my free finance education library. It runs to five volumes, from the whole-economy view in Volume I to household-level detail in Volume V, and every article is written to be read on its own, with worked numbers and primary sources behind the facts.

How the articles are built: each one opens with a plain-words explanation and a short summary, develops the idea with a worked example, and closes with a decision rule, the costliest mistake, a recap and a self-check quiz. The aim is that you can read any single article without having read the others.

Who it is for: students who want the foundations explained properly, professionals who want a precise reference they can check against primary sources, and anyone managing their own money who would rather understand the mechanism than follow a rule of thumb.

What the full article covers

The full article includes worked examples, a recap, a reveal-on-click quiz and the official sources behind every figure.

Volume V: Personal Finance

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The complete article, 30-Year Fixed vs ARM: Which Mortgage Is Better? A 7/6 ARM Case, with every worked example, diagram, quiz and source, is free to read in Volume V, Personal Finance on finolib.com.

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