FIN 351 · Real Estate Principles

Mortgage Cost and Payment Risk

See why fees and the expected payoff date change borrowing cost—and how conventional, interest-only, and Option ARM structures reshape payments and loan balances.

Created by Desen Lin · California State University, Fullerton

Learning map

One loan, several measures of cost and risk

Change any orange-accented assumption first. Every payment, balance, effective rate, curve, and comparison updates immediately.

1 · Contract rate

Determines the scheduled payment and interest charged, but does not summarize up-front borrowing costs.

2 · APR

Converts interest and finance charges into one rate assuming the loan remains outstanding for its full term.

3 · ECB

Recalculates cost for the expected payoff date, spreading up-front charges over the actual holding period.

4 · Payment structure

Lower initial payments may preserve the balance, create negative amortization, and produce a later payment shock.

Mortgage comparison

1. How assumptions change APR and effective borrowing cost

APR prices the full contractual term. ECB uses the same monthly payment but adds the remaining balance at the selected payoff date. Compare Loan A's higher rate and lower fees with Loan B's lower rate and higher fees.

Net proceeds = loan amount × (1 − finance charges)APR uses all scheduled payments; ECB also includes the balance due at early payoff.

Loan A · higher rate, lower fees

Loan B · lower rate, higher fees

Loan A
Loan B
Lower ECB
Effective cost over the payoff horizonAPR is the full-term endpoint of each ECB curve
Loan A ECBLoan B ECBLoan A APRLoan B APR

Moving right spreads the same up-front charges over more years. The vertical marker is the selected payoff year.

Rates at the selected payoff yearNominal annual rates with monthly compounding

APR can reverse a comparison based only on contract rates; ECB can reverse it again when the payoff occurs early.

Payment design

2. Option ARM versus I-O amortizing and conventional mortgages

The same principal can follow very different paths. The Option ARM simulation uses the Chapter 10 simplified minimum-payment rule and recasts at the selected year or when the negative-amortization cap is reached.

Payment = interest + principal amortizationWhen payment is below interest, principal amortization is negative and the loan balance grows.
Option ARM assumptions
Conventional paymentlevel monthly payment
I-O payment change
Option ARM recast
At comparison yearConventionalI-O amortizingOption ARM
Monthly payment pathYear-end scheduled payment
Conventional FRMI-O amortizingOption ARM

The I-O loan jumps when amortization begins. The minimum-payment Option ARM can jump earlier if its balance reaches the cap.

Outstanding loan balanceYear-end balance
Conventional FRMI-O amortizingOption ARMOriginal principal

A balance above the original principal is negative amortization: unpaid interest has been added to principal.

Interpretation

Key takeaways

Rate is not total cost

A lower contract rate may be offset by higher fees. APR makes that tradeoff visible over the full term.

Time changes the ranking

ECB matters when refinancing, selling, or otherwise paying off early. The shorter the horizon, the more heavily up-front charges weigh.

Low payment is not low cost

Interest-only and minimum-payment designs delay principal repayment. An Option ARM may add unpaid interest to the balance and amplify the later recast.