Mortgages: 30 years, dollar by dollar.
The longest, biggest amortizing loan most people will ever sign for. The new math: the principal/interest split per payment, and what it means that early payments are mostly interest.
You sign a 30-year mortgage on a $300,000 house at 7%. The monthly payment is $1,995.91. Five years in, you check your statement and notice something strange: you've made 60 payments totaling about $120,000 — but your remaining balance is still around $282,000.
$120,000 paid · $18,000 of principal gone · $102,000 of interest
That's not a mistake. It's amortization, with the interest piled into the early years on purpose. Each individual payment splits into two parts — mostly interest at first, mostly principal toward the end. This lesson is the math that produces the split, payment by payment.
Two lines, every month, for 360 months.
Month 1 of a $300,000 mortgage at 7% over 30 years. The fixed monthly payment is $1,995.91, but only $245.91 of it knocks down the balance — the other $1,750 is interest on the still-massive principal. That's why early mortgage payments feel like “all interest, no equity.” The split shifts month by month as the balance shrinks.
An amortization schedule tracks every monthly payment of a loan, showing how each payment splits between interest and principal and how the balance shrinks. For one payment: interest portion = balance × (r/12), principal portion = M − interest portion, new balance = balance − principal portion.
Vocabulary you'll see in word problems
- Mortgage A long-term loan secured by real estate. Standard terms are 15 or 30 years; the home itself is collateral.
- Principal/interest split How each monthly payment breaks down. Front-loaded toward interest in early years, back-loaded toward principal in later years.
- Amortization schedule A row-by-row table of every payment, the interest portion, the principal portion, and the remaining balance. The full visual record of how the loan gets paid off.
- Escrow An account the lender holds to pay your property taxes and homeowner's insurance. You pay 1/12 of the annual amount each month as part of your mortgage payment.
- PITI Principal + Interest + Taxes + Insurance — the four components of a typical mortgage payment. When people say "my mortgage" they usually mean PITI.
- Refinancing Replacing an existing mortgage with a new one, usually at a lower rate. Resets the amortization clock.
$300K @ 7%, 30 years, month 1.
"You buy a $300,000 home with a 30-year mortgage at 7% APR (no down payment for simplicity). Compute the monthly payment, total cost over 30 years, and the principal/interest split for month 1."
Apply the L2 amortization formula.
P = $300,000, r = 0.07, t = 30. So r/12 ≈ 0.005833 and n = 12·30 = 360.
Total cost + total interest over the loan.
360 payments at $1,995.91. Then subtract the original principal to isolate interest.
Month 1 interest portion.
The bank charges this month's interest on the current balance. At the start, balance = $300,000.
Month 1 principal portion + new balance.
Whatever's left of M after interest pays down the balance.
Where does it go from here?
Month 2 starts with balance $299,754.09. Run the same arithmetic to see the split begin to shift.
Three problems. Monthly, split, term comparison.
A $250,000 mortgage at 6% APR for 30 years. What's the monthly payment?
A mortgage has a current balance of $180,000 at 6% APR, with a fixed monthly payment of $1,200. For this month's payment, what's the interest portion?
Same $300,000 loan, same 7% APR, but compare a 15-year term to the 30-year case. The 30-year monthly is $1,995.91; what's the 15-year monthly?
Three fast questions before you move on.
Q1. On a mortgage with a current balance of $240,000 and a 6% APR, the interest portion of one month's payment is...
Q2. Doubling a mortgage's term from 15 years to 30 years (same P, same r) makes the monthly payment...
Q3. The principal portion of a single mortgage payment equals...
The interest is front-loaded.
This is the topic finale, so a small celebration is in order: you have now seen every formula in the ALEKS dictionary at work. Topic 3 covered savings/growth; Topic 4 covered loans/debt. The two are mirror images — the same compounding math either grows your account or grows your obligation, depending on which side of the loan you're on.
The week's review pulls all of this together across six questions. Lean on the cheat sheet and the Financial Formulas Calculator, and remember: the per-payment split in this lesson is what review Q5 asks for. Every question you answer this week is one of the three formulas applied to a real loan type.
Back to Topic 4Different angle? Need another rep? These are optional — tap any that look helpful.