Loan Amortization

Loan amortization is a fundamental concept in financial planning, particularly for mortgage analysis, debt management, and client education. The CFP exam frequently tests your ability to calculate payment allocations, remaining balances, and the impact of accelerated payoff strategies.

What Is Amortization?

Amortization is the process of gradually paying off a loan through periodic payments that include both principal and interest. Each payment is divided between:

1. Interest - Compensation to the lender for the use of their money
2. Principal - Reduction of the original loan balance

An amortization schedule is a table showing exactly how each payment is allocated between interest and principal, plus the remaining balance after each payment.

The Fundamental Amortization Relationship

For a fixed-rate amortizing loan:

This occurs because interest is always calculated on the remaining balance. As the balance decreases, less interest accrues, leaving more of each payment available for principal reduction.

Early vs. Late Payment Allocation

Understanding this allocation pattern is critical for client conversations and exam questions:

Early Payments (Front-Loaded Interest)

• A larger portion goes to interest
• Smaller portion reduces principal
• Equity builds slowly initially

Later Payments (Principal-Heavy)

• Smaller interest portion
• Larger principal reduction
• Equity builds rapidly toward the end

Example: $300,000 30-Year Mortgage at 6%

Exam Tip: After 5 years (60 payments) on a 30-year mortgage, only about 6% of the principal has been paid down. After 15 years (180 payments), approximately 23% of principal is paid. This illustrates why early extra payments have the greatest impact.

Calculator Amortization Functions

Your financial calculator can determine interest paid, principal paid, and remaining balance for any payment period or range of periods.

TI BA II Plus AMORT Function:

1. First, calculate PMT using standard TVM keys
2. Press 2nd AMORT
3. Enter P1 (starting payment number)
4. Enter P2 (ending payment number)
5. Navigate through: BAL (balance), PRN (principal paid), INT (interest paid)

Example Calculation:

For a $200,000 mortgage at 5% for 30 years, find how much interest and principal are paid in Year 1.

Step 1: Calculate Payment

• N = 360
• I/Y = 5/12 = 0.4167
• PV = 200,000
• FV = 0
• Solve: PMT = -$1,073.64

Step 2: Use AMORT for Payments 1-12

• P1 = 1, P2 = 12
• BAL = $196,878.67 (remaining balance after 12 payments)
• PRN = $3,121.33 (principal paid in Year 1)
• INT = $9,762.35 (interest paid in Year 1)

Impact of Extra Principal Payments

One of the most powerful client conversations involves showing the impact of additional principal payments. Extra payments applied to principal:

1. Reduce total interest paid over the life of the loan
2. Shorten the loan term (payoff earlier)
3. Build equity faster

Example: Extra $200/Month on a $300,000 Mortgage at 6%

The client pays an extra $200 x 282 months = $56,400 but saves $91,391 in interest, a net benefit of nearly $35,000.

Calculating Extra Payment Scenarios

To calculate new payoff time with extra payments:

TI BA II Plus Method:

1. Use original loan parameters
2. Increase PMT by the extra amount
3. Solve for N (new number of payments)

Example:

• Original: PV = 300,000, I/Y = 0.5, PMT = -1,798.65, FV = 0
• With extra: PMT = -1,998.65, solve for N = 282 months

Mortgage Refinancing Analysis

Refinancing replaces an existing mortgage with a new one, typically to:

• Obtain a lower interest rate
• Change the loan term
• Switch from ARM to fixed rate
• Access home equity (cash-out refinance)

Refinancing Decision Framework:

Break-Even Analysis:

Break-Even Months = Closing Costs / Monthly Savings

Example: Refinancing Calculation

Current mortgage: $286,424 remaining balance at 7%, 26 years left Payment: $1,995.90/month

New mortgage: $289,424 (includes $3,000 closing costs) at 5%, 20 years New payment: $1,910.07/month

Monthly Savings: $1,995.90 - $1,910.07 = $85.83 Break-Even: $3,000 / $85.83 = 35 months (about 3 years)

Total Interest Comparison:

• Current: $1,995.90 x 312 - $286,424 = $336,296 remaining interest
• New: $1,910.07 x 240 - $289,424 = $168,993 total interest
• Net Savings: $167,303 in interest, plus loan paid off 6 years earlier

Exam Tip: Refinancing questions often require calculating remaining balance on current loan, then setting up the new loan including closing costs. Do not forget to add closing costs to the new loan amount if they are being financed.

Types of Amortizing Loans

The 28/36 Rule Connection

Amortization knowledge connects to the housing and debt ratios:

28% Rule: Monthly housing costs (PITI) should not exceed 28% of gross monthly income

• P = Principal portion of mortgage payment
• I = Interest portion of mortgage payment
• T = Property Taxes (monthly)
• I = Insurance (homeowners, monthly)

36% Rule: Total debt payments should not exceed 36% of gross monthly income

• Housing costs (28%) + All other recurring debt

Example: Client gross monthly income: $10,000 Maximum housing payment: $10,000 x 0.28 = $2,800 Maximum total debt: $10,000 x 0.36 = $3,600 Maximum non-housing debt: $3,600 - $2,800 = $800

Practical Application: Debt Payoff Strategies

Understanding amortization helps evaluate debt payoff strategies:

Debt Avalanche Method

• Pay minimums on all debts
• Extra payments to highest interest rate debt first
• Mathematically optimal, saves most interest

Debt Snowball Method

• Pay minimums on all debts
• Extra payments to smallest balance first
• Psychologically motivating, quick wins

Which to Recommend? For purely mathematical efficiency, the avalanche method wins. However, behavioral finance research shows the snowball method often leads to better outcomes because the psychological momentum of paying off debts keeps clients motivated.

Key Amortization Formulas

While the calculator handles these, understanding the relationships helps:

Payment Calculation: PMT = PV x [i(1+i)^n] / [(1+i)^n - 1]

Remaining Balance at Period k: Balance = PV x [(1+i)^n - (1+i)^k] / [(1+i)^n - 1]

Interest in Period k: Interest = Previous Balance x i

Principal in Period k: Principal = PMT - Interest

Common Exam Question Types

1. Calculate monthly payment - Standard TVM
2. Find remaining balance at a specific point - AMORT function
3. Determine interest/principal paid over a period - AMORT function
4. Compare payoff scenarios with extra payments
5. Evaluate refinancing decision - Break-even analysis
6. Apply housing ratios to determine qualifying loan amount