# Relationship between down payment and mortgage interest

I just got a new job in a new city in Ohio (United States), and my partner and I want to buy a home roughly a year from now. We have a year to save up, and I am making a financial model to look at the pros and cons of putting down a big down payment vs doing other things with the money, like paying down student loans.

How can I quantitatively estimate the relationship between home mortgage interest rates and down payments? I know that they are connected, but I can't find any quantitative source.

• Possible duplicate of First time home hunters. Pay debt or save for down payment Apr 6, 2019 at 18:14
• @Yoozer8 The question you linked is asking for advice on how to balance specific types of debt, and wants the answerer to do the math for them. The answers to that question do not help me answer mine. Apr 6, 2019 at 20:28

First, the main benefit of a larger down payment is avoiding private mortgage insurance (PMI).

The effect on the interest rate is generally small, if you have good credit and are putting at least 5% down (less than 95% loan-to-value). See here for an idea of how federal mortgage agencies price the effect on loan risk (which passes through to your interest rate).

Apart from PMI and interest rate, increasing the down payment obviously reduces the loan amount for a given house, reducing the total interest you will pay. It is similar to paying down any other loan, so you would prioritize loans with the highest rate (or keep the money invested if you can earn an even higher rate).

EDIT: I agree there are some bumps in the LLPA table that seem anomalous. My main point is that the down payment effect on risk pricing is quite small and can probably be neglected in your modeling. According to the linked article, the percentage in the table is a one-time charge on the loan amount (but incorporated into your loan costs, not owed by you up front). Thus, roughly, you'd divide it by something like the number of years in the mortgage to get an effective interest rate delta.

Most important in choosing the down payment is to put enough down to avoid PMI if you can, and to compare your likely mortgage interest rate with other loans and investments. The nice thing is that mortgages generally have no prepayment penalty, so if you end up wishing you had put more down to reduce the loan balance, you can make one or more larger payments and get a similar total-interest-saving effect.

• But also the borrower will typically not see the affect of down payment on interest directly. The typical way they can benefit from a lower rate due to risk based pricing is by shopping around. It wouldn’t hurt to ask the lenders directly about their risk based pricing though since it may help with negotiating. Also, Bob, if applicable to you, see ways to raise your credit score which can make more difference as nanoman said. Apr 6, 2019 at 9:10
• This answer is pretty useful, but I am having a little trouble turning this into an actual formula I can put into my financial model. If I understand right, there is some base rate, to which you add the LLPA, plus probably some other random stuff. Apr 6, 2019 at 15:00
• Also, why is the LLPA higher with a 75-80% LTV range than a 80-85% range? Apr 6, 2019 at 15:01