Lesson 2 of 25 · 6 min

Principal and interest, split

The first payment is mostly interest because the whole principal is still sitting there.

Inside principal-and-interest, one cash figure hides two legs. Interest is this month's accrual on the unpaid balance. Principal is whatever is left of the installment after that interest is taken. Track 1 lesson 14 is daily accrual: the charge is computed on that day's balance. This lesson does not re-teach that clock. It uses a monthly tick of the same machine. The first month's balance is the whole loan, so the first month's interest is almost the whole payment.

PMT = P × r × (1+r)^n / ((1+r)^n − 1), r = APR / 12

PMT: The fixed monthly principal-and-interest installment.
P: The principal being financed.
r: The monthly rate, APR divided by 12.
n: The number of months in the term.

Marrow Street Mortgage writes $287,400 at an illustrative 6.15 percent for 360 months. The payment is $1,750.92. First-month interest is $287,400 × 0.0615 ÷ 12 = $1,472.93, which is 84.1 percent of the payment. Principal is $1,750.92 − $1,472.93 = $278.00. Across year 1 the twelve payments total $21,011.06. Interest takes $17,579.44, or 83.7 percent. Principal takes $3,431.62. The remaining balance is $283,968.38.

Track 5 lesson 15 reconstructs an interest leg by hand so the statement's single figure can be split. The same reconstruction sits inside every mortgage payment. The cash did not change. The split did, because the unpaid balance did. Early months are interest-heavy because P is still almost P.

The payment is fixed. The split is not. Interest is charged on whatever principal is still there, which at the start is nearly all of it.

Key terms

Interest leg: This month's accrual on the unpaid balance, taken out of the installment first.
Principal leg: Whatever remains of the installment after this month's interest is taken.
Remaining balance: Unpaid principal after a stated number of payments. The next month's interest is charged on this figure.

Worked example

Month one, then year one

Marrow Street Mortgage. Principal $287,400, illustrative 6.15 percent, 360 months. Payment $1,750.92.

First-month interest: $1,472.93
First-month principal: $278.00
Year 1 paid: $21,011.06
Year 1 interest: $17,579.44
Year 1 principal: $3,431.62
Remaining after year 1: $283,968.38

Twelve payments of $1,750.92 moved $3,431.62 of principal. The rest was interest on a balance that had barely shrunk.

Check yourself

Principal $214,800, illustrative 5.85 percent, 360 months. What is the payment, the first month's interest, and the first month's principal?

Early mortgage interest is the everyday version of an interest leg that dwarfs principal, the reconstruction Track 5 lesson 15 does by hand. Open How to recompute an interest leg by hand →

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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.