Calculating the Initial Payment of a Graduated Payment Mortgage

Summary

The document asks how to find the starting monthly payment for a 30-year graduated payment mortgage. Its example uses a 12% annual rate, monthly payments, four annual increases of 7.5%, and payments held constant after the fourth increase. It presents a present-value equation that discounts each payment block separately, with the later blocks scaled by the accumulated payment increases.

The question compares this setup with a growing-annuity formula and asks why that simpler expression does not produce a sensible result. No answer or worked calculation is provided, so the document does not resolve how the two formulations relate. The example also leaves conventions such as the timing of payment increases and the precise rate-period conversion implicit. It serves as a focused question about valuing a piecewise payment stream, rather than a complete mortgage calculation method.

Key ideas

• The example mortgage has monthly payments over 30 years and four annual payment increases.
• Each payment block is discounted to the present, while later blocks are scaled for prior increases.
• The author asks whether a growing-annuity formula can calculate the initial payment.
• The document provides no worked solution or resolution of the formula mismatch.

Tags

# How to calculate the initial payment of a graduated payment mortgage (GPM). Real estate Mortgage analysis


# How to calculate the initial payment of a graduated payment mortgage (GPM). Real estate Mortgage analysis












My professor used this: 12%, monthly-pmt, 30-yr GPM with 4 annual step- ups of 7.5% each, then constant after year 4:

$$L=PMT \left[ PV(0.01,12,1) + \frac{1.075}{1.01^{12}}PV(0.01,12,1) + \frac{1.075^2}{1.01^{24}}PV(0.01,12,1) \\ + \frac{1.075^3}{1.01^{36}}PV(0.01,12,1) + \frac{1.075^4}{1.01^{48}}PV(0.01,312,1)\right]$$

I just don't understand why would one multiply the present value of 1$ with the actual present value of the growth of the dollar and so forth.

Why isn't this working

$$PMT_1 = L\bigg/\left(\frac{1-((1+g)/(1+r))^N}{r-g}\right)$$

This formula is so much more logical but I'm getting something that doesn't make sense at all.

http://www.financeformulas.net/Growing-Annuity-Payment.html

It's so confusing for me now.

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