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My company is developing a product that helps people project out what-if scenarios for paying down their student loan debt. One of the government options for paying off debt is called the "graduated" program, under which the beginning payment is known, and every two years the required payment increases such that the timeline for payoff fits within a desired term, say 30 years.

We've been unable to find a documented formula for this payment schedule. Does anyone have an idea or starting point?

Example: $100,000 in total debt at 6.5% interest. Desired term is 30 years. Input variables: total debt, yearly interest rate, desired term

Payment for years 1-2 is always: debt * yearly interest rate / 12

From there the required payment goes up every two years, so years 3-4, 5-6, etc. until the principal balance reaches zero at the end of the desired term (30 years.)

Note: desired term is not always evenly divisible by 2.

Output: What are the required payments for each remaining two year bracket?

Chad P
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1 Answers1

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The loan debt (present value) and the present value of the pay-offs have to be equal. If the pay-offs increseases every year by the amount of d, then the formula is:

$\text{loan debt}=r\cdot \frac{q^n-1}{i\cdot q^n}\cdot \frac{d}{i}\cdot \left(\frac{q^n-1}{i\cdot q^n}-n\cdot q^{-n} \right)$

i=interest rate

q=1+i

r=amount of pay-off without any change

callculus42
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