Amortization and payments

An amortising loan is paid off gradually: each payment covers that month's interest and repays a little principal. With the same payment every month, the early payments are mostly interest, and the share of principal grows as the balance falls.

The monthly payment for a loan L at a monthly rate r (the annual rate ÷ 12) over n months is L × r ÷ (1 − (1 + r)^−n). A $4,000,000 loan at 6.5% a year over 30 years (360 months):

loan, annual_rate, years = 4_000_000, 0.065, 30
r, n = annual_rate / 12, years * 12
payment = loan * r / (1 - (1 + r) ** -n)
print(f"monthly ${payment:,.2f}, yearly ${payment * 12:,.0f}")
print(f"first month: interest ${loan * r:,.2f}, principal ${payment - loan * r:,.2f}")

Commercial loans often have a term shorter than the amortisation: payments are worked out as if over 30 years, but the loan is due after 10. Whatever's still owed then is due in one go, the balloon payment, which the borrower usually pays by refinancing or selling. After 10 years of the loan above, about $3.39 million is still owed.

loan, r, n = 4_000_000, 0.065 / 12, 360
payment = loan * r / (1 - (1 + r) ** -n)
balance = loan
for month in range(120):
    balance -= payment - balance * r
print(f"balance after 10 years: ${balance:,.0f}")

Interest-only (IO) loans pay only interest for some or all of the term: $4,000,000 × 6.5% = $260,000 a year, against about $303,400 amortising. That lowers the payment and raises DSCR, but nothing is repaid, so the whole loan is due at the end. Lenders often test DSCR on an amortising payment even when the loan has an interest-only period, so the IO doesn't flatter the numbers.

Refinancing risk is the big one: at maturity, the borrower needs a new loan for the balloon. If rates are higher or the value lower by then, the new loan may not be big enough to pay off the old one.