Lesson 11 of 25 · 6 min

Reading an amortization schedule

The schedule is a chain of remaining balances; each row is last month minus this month's principal.

An amortization schedule is a chain of remaining balances. Each row takes last month's unpaid principal, charges this month's interest on it, subtracts that interest from the fixed installment, and writes a new remaining balance. Track 5 lesson 16 checks a balance chain on a securities-backed line: opening plus draws minus repayments plus interest equals closing. A mortgage schedule is that chain with no draws, one repayment a month, and interest taken from the installment before principal.

remaining after k payments = P × ((1+r)^n − (1+r)^k) / ((1+r)^n − 1)

P: The original principal.
r: The monthly rate, APR divided by 12.
n: The original term in months.
k: How many payments have been applied.

Same Marrow Street book as lesson 2: $287,400 at 6.15 percent for 360 months, payment $1,750.92. After 60 payments the remaining balance is $267,929.21. Principal repaid is $287,400 − $267,929.21 = $19,470.79. Total paid is the exact installment × 60 = $105,055.30. Interest paid is $105,055.30 − $19,470.79 = $85,584.51.

After 180 payments the remaining balance is $205,511.54. Principal repaid is $81,888.46. Total paid is $315,165.91. Interest paid is $233,277.45. Fifteen years of the schedule have retired 28.5 percent of the original principal and have paid nearly three times that amount in interest. The chain is mechanical. Every row is the formula above, or the previous row minus this month's principal leg.

The schedule is not a forecast of the house. It is a chain of unpaid principal at a constant r. Check it the way Track 5 lesson 16 checks a line: each closing must equal the next opening.

Key terms

Amortization schedule: The row-by-row chain of remaining balances, interest legs and principal legs at a constant r.
Principal repaid: Original P minus remaining balance after k payments.
Interest paid: Total of installments to date minus principal repaid. The cumulative interest leg.

Worked example

Two marks on one chain

Marrow Street Mortgage. $287,400 at 6.15 percent, 360 months, payment $1,750.92.

After 60 payments, remaining: $267,929.21
Principal repaid by month 60: $19,470.79
Total paid by month 60: $105,055.30
Interest paid by month 60: $85,584.51
After 180 payments, remaining: $205,511.54

Five years retired $19,470.79. Fifteen years retired $81,888.46. The chain is slow at the start because the interest leg is large while P is large.

Check yourself

Same $287,400 at 6.15 percent, payment $1,750.92. After 24 payments the remaining balance is $280,319.67. What is principal repaid, total paid, and interest paid?

The schedule is the everyday version of a balance chain, the check Track 5 lesson 16 teaches on a securities-backed line. Open How to check a balance chain →

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Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.