Lecture 8: Amortizing Fixed-Rate Mortgages

Fixed-Payment Loan Formula

PB = FP × (1/i) × [1 − 1/(1+i)ⁿ]

PB = principal balance now

FP = fixed monthly payment

i = monthly rate

n = months remaining.

Monthly Rate

Annual rate ÷ 12 (6% annual → 0.5% monthly)

Mortgage rates are always quoted annually but applied monthly

Interest Portion of a Payment

i × (principal balance at the start of that month). Month 1: 0.5% × $200,000 = $1,000.00

Principal Portion of a Payment

FP − interest portion

Month 1: $1,199.10 − $1,000.00 = $199.10

The two always sum to $1,199.10

How to Find the Remaining Balance

Plug the remaining number of months into the same formula

After 1 payment (n = 359): $199,800.90

After 12 payments (n = 348): $197,543.99. After 360 payments (n = 0): $0

Front-Loading of Interest

Early payments are mostly interest, late payments mostly principal, because the interest charge is a fixed % of a shrinking balance

Payment 1: $1,000 interest / $199 principal

Payment 360: $5.97 interest / $1,194.16 principal

Total Cost

Over 30 years: $200,000 principal + $231,677.03 interest = $431,677.03 total. You pay more in interest than you borrowed

Pmt / Principal / Interest / Cumulative Prin / Cumulative Int / Prin Bal Columns

Payment number, principal portion, interest portion, cumulative principal paid, cumulative interest paid, and remaining principal balance

Prepayment of a Principal Balance

With a prepayment option, paying the remaining principal balance in cash ends the loan

Prepayment Penalty Terms

Penalty on any prepayment, penalty only on refinancing (none if you sell), or no penalty at all if you negotiate well