How should loan amounts be calculated relative to house purchase price?

Assuming from your opening sentence that you are buying a completed (but brand new) home from a builder, the mortgage works like any other mortgage. You and the seller will agree on a sale price. You will (likely) put some money down. The opening balance for your mortgage loan will be the sale price minus the amount you put down.

The only real difference with a newly built home is that builders sometimes play games with buckets of money for various reasons. This can sometimes mean that money is changing hands in a way that isn't as transparent as "sale price minus down payment equals loan balance." This is frequently done when it comes to paying for upgrades compared to the standard design for the home.

For instance, if you have decided on an upgrade (finishing a basement, adding an extra bathroom, adding a deck, so on), the builder may sometimes expect payment for these items outside of the mortgage as if you had hired them as a contractor to do these improvements to a home you already owned. Or they may bake the costs in to the sale price. Or they may do something that is a mix of both. These upgrades sometimes come with their own deposits which are paid directly to the builder before the mortgage closes, and those deposits - or the total cost for the upgrades or the value they add to the home - are not inherently included in the mortgage paperwork.

So, ultimately, you may be buying a home for $200,000 but paying for it in many different ways. For the sake of argument, let's assume the base model sells for $180,000 and you've elected for $20,000 in upgrades, and you're putting $50k in cash into the deal. You could end up in any of the following situations:

• You've bought a home for $200,000 with a $50,000 down payment - 25% - and will have a mortgage balance of $150,000 and an LTV (loan to value) of 75% as of your closing. The builder bakes in the cost of the upgrades, does them before you close, and everything is straightforward.
• You've bought a home for $180,000 with a $30,000 down payment - 17% - and will have a mortgage for $150,000 but your LTV is 83%, so now your lender is requiring PMI. Your builder immediately does the improvements, which you've already paid them for (the other $20k of your $50k spent out of pocket), you petition your bank that the value of your home has increased, they send out an appraiser and decide that your home is now worth $200,000 - which implies an LTV of 75% - and you can remove the PMI. Or maybe they decide it's not worth that much. Maybe it only assesses at $190,000 and you're required to keep the PMI.
• You've bought a home for $180,000 with a $50,000 down payment (27%) and will have a mortgage for $130,000 and an LTV of 73%, and you'll immediately owe your builder $20,000 for those upgrades, which will be paid off the books of the home sale. Then, you and the builder both conveniently "forget" to tell anyone about the upgrades, the tax assessor never finds out about them, and your property taxes are based on a $180,000 value instead of the correct $200,000 value.

Or maybe you'll end up in some other mix of the above scenarios. The key point is: paying for a newly constructed home, including upgrades, can be complex, and the numbers for scenarios that sound similar can shake out in very different ways. It pays to discuss all of this with both your builder and your lender before signing anything or giving any money to anyone, in order to make sure everyone is on the same page. If you're already under contract and money is already changing hands, ask your builder and your lender to explain the numbers and how things will look at closing if you're not already sure. And read your contract yourself to make sure everyone is telling you the full story.