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Graduated Payment Loan Calculator

Enter your loan details and graduation schedule to estimate the graduated payment stream.

How it is calculated

With i = annual rate ÷ 100 ÷ 12, n = term in months, g = graduation rate ÷ 100 and k = graduation years, the payment is P × (1 + g)j in year j + 1 for j = 0 … k − 1, and P × (1 + g)k for the remaining n − 12k months. The tool solves for the starting payment P so that the present value of all these payments at the monthly rate equals the loan amount: P = principal ÷ [Σj=0…k−1 (1 + g)j × a(12) × v12j + (1 + g)k × a(n − 12k) × v12k], where a(m) = (1 − (1 + i)−m) ÷ i (or m at 0%) and v = 1 ÷ (1 + i). It shows the starting payment, the year-2 payment P × (1 + g) and the final level payment P × (1 + g)k. FHA's Section 245 rule (24 CFR 203.45) allows 2.5%, 5% or 7.5% for 5 years or 2% or 3% for 10 years; the tool accepts other rates too. The term and graduation years must be whole years, graduation years at least 1 and shorter than the term, and rate, graduation rate and term are capped at 100; anything else shows no result. The balance and the negative amortization of the early years are not shown, and a lender's figures can differ slightly through rounding, fees and mortgage insurance.

Worked example

Borrow $200,000 at 6% for 30 years, with payments rising 7.5% a year for 5 graduation years. Monthly rate is 0.005 and n is 360; the standard level payment would be about $1,199.10. The tool finds the starting payment P that repays the loan: P for months 1–12, P × 1.075 for months 13–24, and so on, up to P × 1.0755 from month 61 to month 360, with every payment discounted at 0.5% a month adding up to $200,000. That gives a starting payment of $889.83 (74% of the level payment), $956.56 in year 2 and a final payment of $1,277.46 from year 6 on, above the standard $1,199.10. In the early years the payment is below the monthly interest of $1,000, so the unpaid interest is added to the balance.

Try this example →

Common mistakes

  • Treating the start payment as an exact quote. The tool solves the schedule from your inputs; a lender adds mortgage insurance, taxes and its own rounding, so ask for the actual figures.
  • Entering the graduation rate as a monthly or total rise. It is a yearly rate: 7.5 means each step is 7.5% above the last one.
  • Comparing the start payment with the interest. In the first years it is often below the monthly interest, so the balance grows (negative amortization) before the later, higher payments pay it down.
  • Entering as many graduation years as the loan has, such as 30 on a 30-year loan. A level period has to follow the steps, so the tool shows no result.
  • Setting graduation years to 0 to see a level payment. The tool needs at least one graduation year and shows no result for 0; use a standard loan calculator for a flat payment.

Sources

About this calculator

A graduated payment mortgage (GPM), historically formalized in the U.S. as FHA Section 245 loans, is designed for borrowers who expect their income to rise over time: instead of a level payment from day one, the monthly payment starts noticeably lower than a standard fully amortizing payment and then steps up each year during a graduation period, typically 5 to 10 years, before leveling off for the rest of the term.

The FHA rule (24 CFR 203.45) lets the payment rise each year for five years at 2.5%, 5% or 7.5%, or for ten years at 2% or 3%, and then stay level. This calculator takes your graduation rate and years and solves for the starting payment that makes the whole schedule (the stepped payments, then the level payment for the rest of the term) repay the loan at its interest rate. For a 6.5% 30-year loan with 7.5% steps over 5 years it comes out at about 74% of the standard level payment. Because early payments can be lower than the interest actually accruing, GPMs commonly involve negative amortization in the first years — the loan balance temporarily grows before the higher later payments pay it back down.

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