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We recently closed on a house with a primary market player and in the contract it gave the standard Your loan can be sold at any time yadda, yadda, yadda... and this is fine.

Fast forward 5.5 weeks and our mortgage has been sold to a secondary market player.

How could this possibly be financially beneficial for the original loan holder?

Are they truly making enough money from the mortgage fees and first payment's interest to to warrant their need to clear up their credit line for new mortgages?

Are mortgages always sold for less than the remaining principal?

Let's assume:

House: $150,000
Down: 20% ($30,000)
Mortgage: $120,000
Interest: 3.75%
Term: 30-year fixed
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Are mortgages always sold for less than the remaining principal?

No, they're almost always sold for more than that. The buyer will take a loss if the homeowner pays off the loan immediately, but that's very unlikely. The buyer is hoping that the owner will payoff the loan as scheduled and they'll make a tidy profit from the interest charged.

The originator now makes their profit immediately and has their capital back so they can make more loans.

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our mortgage has been sold to a secondary market player.

There are multiple ways in which the deal is struck. At times the risk of default is with Original FI [with recourse], at times it is with secondary FI [without recourse]. The rate can be discounted. So the Original FI collects the EMI as per 3.75 and pays to the secondary FI at 3.25. Or it can also be one time fixed amount.

How could this possibly be financially beneficial for the original loan holder?

As indicated, there are multiple ways the Original FI makes money, either one time or over the period, depending on how the deal is struck.

Are they truly making enough money from the mortgage fees and first payment's interest to to warrant their need to clear up their credit line for new mortgages? Are mortgages always sold for less than the remaining principal?

No broadly speaking the mortgage fees cover the cost for initiating the loan. There may be a very small amount banks may make. This is incidental. The actual money is made in the interest that is collected every month.

If a Bank as say 5 loans for 100K each. It is very reputed brand and 10 people need 100K loans. Then it makes sense for the First FI to give loan to 5 people for 100K each, and sell this at profit to secondary FI. Take the 100K * 5 and give it off to new 5 people. Effectively making more money on the original 500K the bank had.

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The mortgage broker makes money from the mortgage originator, and from closing fees. All the broker does is the grunt work, mostly paperwork and credit record evaluation. But there's a lot of it. They make their money by navigating the morass of regulations (federal, state, local) and finding you the best mortgage from the mortgage lender(s) they represent. They don't have any capital involved in the deal. Just sweat equity.

Mortgage originator is the one who put up the capital for you to borrow. They're the ones who get most of the payments you send in. They sell the mortgage if they receive what they consider an equitable offer. Keep in mind that the mortgage, from the lender's point of view, is made up of three parts. The capital expenditure, the collateral, and the cashflow. The present value of the cashflow at the rate of the loan is greater than the capital expenditure. Any offer between those two numbers is 'in the money' for them, and the next owner, assuming no default. But the collateral makes up for the chance of default, to an extent.

There's also a mortgage servicing company in many cases. This doesn't have to be the current holder of the loan.

Study "the time value of money", and pay close attention to the parts about present value, future value, and cash flow and how to compare these.

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