| Monthly Payment | — |
| Total Cash Collected | — |
| Total Profit | — |
| Discount from UPB ($) | — |
| Discount from UPB (%) | — |
| Balloon Payment Used | — |
Worked Example
Suppose you can buy a performing note with a $100,000 UPB (unpaid principal balance), a 7% annual interest rate, and 240 months remaining, for a price of $80,000. What yield does that price produce?
- Find the borrower's monthly payment. The monthly rate is
0.07 / 12 = 0.00583333…. The fully amortizing payment isP = 100,000 × 0.00583333 / (1 − (1.00583333)−240). The discount factor(1.00583333)−240 = 0.2476020…, so the denominator is0.7523980…, giving a payment of $775.30 per month (exactly $775.2989… before rounding). - Lay out your cash flows. You pay $80,000 today and receive $775.30 per month for 240 months. Total cash collected:
$775.2989… × 240 = $186,071.74. Total profit:$186,071.74 − $80,000 = $106,071.74. - Measure the discount. You are paying $80,000 for a $100,000 balance — a $20,000 discount, or 20% off UPB ("80 cents on the dollar").
- Solve for the yield. Find the monthly rate
iwhere the present value of 240 payments of $775.2989… equals $80,000:80,000 = 775.2989 × (1 − (1+i)−240) / i. There is no algebraic solution, so the calculator iterates with Newton–Raphson. It converges to a monthly rate of0.0083849…(0.83849% per month). - Annualize. Multiply by 12:
0.0083849 × 12 = 0.100619, an annualized nominal yield of 10.062%.
So a 20% discount turns a 7% note into a 10.062% yield — and that yield only improves if the borrower pays off early, because the full $100,000 balance is owed no matter what you paid.
How the Math Works
Step 1 — Monthly payment. The note's payment is computed from the UPB, the monthly rate i = annual rate / 12, and the remaining term n using the standard amortization formula:
P = UPB × i / (1 − (1 + i)−n)
If the rate is 0%, the formula reduces to P = UPB / n.
Step 2 — Cash flow schedule. With no balloon, the schedule is simply n equal payments of P. With a balloon at month m, the payment is still computed on the full amortization, but the schedule truncates at month m: you receive m regular payments plus the balloon. If you leave the balloon amount blank, the calculator uses the exact remaining balance at month m:
B = UPB × (1 + i)m − P × ((1 + i)m − 1) / i
Step 3 — Solve the yield. The yield to maturity is the monthly internal rate of return y that makes the present value of the cash flows equal to the price paid:
Price = P × (1 − (1 + y)−m) / y + B × (1 + y)−m
(with m = n and B = 0 when there is no balloon, and PV = P × m handling the y = 0 edge case). This equation has no closed-form solution, so the calculator solves it numerically:
- Newton–Raphson: starting from the note's monthly rate, iterate
y → y − f(y) / f′(y)wheref(y) = PV(y) − Price, until the step is smaller than 1×10−9 monthly. - Bisection fallback: if Newton's method stalls or steps out of bounds, the solver brackets the root between −0.99 and 10.0 annual (−0.0825 and 0.8333 monthly) and bisects, since
PV(y)is strictly decreasing iny.
The result is reported as the annualized nominal yield — the monthly rate multiplied by 12, the convention used in the note-buying industry (matching how the note's own interest rate is quoted). It is not a compounded effective annual rate, which would be slightly higher.
Assumptions and limitations. The calculator assumes the borrower pays every payment on time and in full, payments are monthly in arrears, and there are no servicing costs, prepayments, or defaults. Intermediate values are never rounded — only the displayed results are. Real-world returns depend on borrower performance, servicing fees, and collection costs.
Frequently Asked Questions
How do you calculate yield on a mortgage note?
First compute the note's monthly payment from its unpaid principal balance (UPB), interest rate, and remaining term using the standard amortization formula. Then solve for the monthly discount rate that makes the present value of all remaining payments (plus any balloon) equal to the price you paid. Multiply that monthly rate by 12 to get the annualized nominal yield. Because there is no closed-form solution, the rate is found numerically — this calculator uses Newton–Raphson iteration with a bisection fallback.
What is yield to maturity on a note?
Yield to maturity (YTM) is the annualized rate of return you earn if you buy the note at a given price and hold it while the borrower makes every scheduled payment through the end of the term (or through the balloon date). It is the internal rate of return (IRR) on your purchase: the discount rate at which the present value of the remaining cash flows exactly equals your purchase price. When you buy a note at a discount to its UPB, your yield is higher than the note's face interest rate.
What discount should I pay for a note?
Work backward from your target yield. Decide the annualized return you need for the note's risk — performing first-lien notes often trade to yields in the 8–12% range, while riskier or non-performing paper demands much more — then pay the price that produces that yield. For example, a $100,000 UPB note at 7% with 240 months remaining priced at $80,000 (a 20% discount) yields about 10.06%. The longer the remaining term and the lower the face rate, the deeper the discount needed to hit a given yield.
Does yield change if the borrower pays off early?
Yes — when you bought the note at a discount, an early payoff raises your realized yield. The borrower owes the full remaining principal balance regardless of what you paid, so an early payoff collapses your discount into profit sooner. In the default example, paying $80,000 for a $100,000 UPB note yields 10.06% if held to maturity, but if the borrower refinanced after one year your realized return would be far higher because you would collect nearly the full $100,000 in just 12 months. The reverse is true for notes bought at a premium.
What is UPB (unpaid principal balance)?
UPB stands for unpaid principal balance — the amount of principal the borrower still owes on the note today. It excludes future interest. UPB is the basis for note pricing: buyers typically quote prices as a percentage of UPB (for example, "80 cents on the dollar" means paying 80% of UPB), and the discount from UPB is what drives the yield above the note's face interest rate.
Why is my yield higher than the note's interest rate?
Because you paid less than the unpaid principal balance. The borrower's payments were calculated on the full UPB at the note rate, but your return is measured against the smaller amount you actually invested. The same monthly payment stream measured against a smaller purchase price produces a higher rate of return. If you paid exactly the UPB, your yield would equal the note rate; pay a premium above UPB and your yield drops below it.
How does a balloon payment affect the yield on a note?
A balloon pulls a large lump of principal forward to the balloon date instead of spreading it across the full amortization. If you bought the note at a discount, receiving principal sooner raises your yield, because the discount is recovered over fewer months. The trade-off is reinvestment and default risk concentrated at the balloon date — the borrower must refinance or pay off the balance in one payment.