Finding a lender to provide a mortgage loan for less than $50,000: It's a challenge faced by a surprising number of people, and one that's often tough to solve.

Sandy Smith of Yes, I Am Cheap brought this issue to our attention when she presented us with a challenge via Twitter:

@gobankingrates @mybanktracker I challenge you both to show banks & rates offering mortgage loans of $50K and less! Under served market!

Under served, indeed. After some research on a few lenders and a call to a Coldwell Banker's mortgage representative (who promised an agent would follow up with me within 24 hours, but never did), I was left without any clear answers, but more determined than ever to find them.

Who Needs Such Small Home Loans Anyway?

This was my first thought. Spending most of my life within the expansive, densely populated and inflated housing market that is Los Angeles County -- namely, the South Bay's "Beach Cities" -- I often forget that half-million dollar homes are not the norm throughout most of the country. According to Trulia.com, the median sales price for a single-family home in Los Angeles today is $551,000.

A few hours away in the more isolated community of Barstow, however, the median sales price is just $77,500.

Homeowners living in small towns or depressed local economies, where property values are quite low, don't need to borrow hundreds of thousands of dollars to buy property -- they only need as much as someone looking to buy a higher-end new car.

Then there are those homeowners who might have secured their loans 15 or 25 years ago, have paid down most of the principal balance on their mortgages, yet want to take advantage of today's amazing mortgage rates by refinancing.

Unfortunately, whether you want to borrow or refinance a mortgage of just $50,000 or less, few lenders are willing to approve it.

Why Lenders Don't Like Providing Small Mortgage Loans

So why is it so difficult to find a lender offering small mortgage loans under $50,000 in the first place? Generally, it's just not worth it to the bank (or the borrower, in most cases).

That's because whether your mortgage is for $50k or $500k, loan origination and servicing costs are about the same. A loan of several hundred thousand dollars over a couple of decades provides the lender a nice profit from interest, while a much smaller loan requiring the same amount of money and effort to fund it yields significantly less. Often, it's not cost-effective for a bank to provide such a small home loan.

If lenders lose money providing extremely small home loans, they are certainly not going to go out of their way to advertise their availability, much less the higher rates associated with these loans. That does not mean, however, that there are no lenders out there who will provide one.

How to Get a Small Home Loan and Alternatives for When You Can't

Just because these small home loans are uncommon doesn't necessarily mean they don't exist. If you need financing for a home that doesn't cost very much, you might be able to get it if you're willing to put in the work.

Reach Out to Local Banks and Credit Unions

Don't expect to walk into a Bank of America or Chase mortgage office and be approved for a $50k mortgage. To find small home loans, you have to go to small institutions.

Your first stop should be your local bank; an existing relationship with a community bank or membership with a credit union is a great in to negotiating a small home loan. Financial institutions are much more willing to work with customers who have proven their loyalty and responsibility with money.

If you don't bank with a community institution, however, or you do, but are rejected for a loan, you should continue to meet with representatives from local banks and credit unions near you and have them review your financial situation (just don't let them all run your credit!) to find out if a small mortgage loan is a possibility. Keep in mind, it could take some time before finding a lender who is willing to work with you.

What to Do When No One Will Give You a Small Mortgage Loan

If you've tried contacting local lenders without any luck, it's time to find alternative ways of funding your home purchase.

Personal Loans

Rather than obtaining a mortgage loan, you can instead finance your home purchase using a personal loan. There are many types of personal loans, ranging from secured loans from major banks, to dangerous, extremely high interest payday loans. Obviously, if you decide on a personal loan, it's important that the terms are manageable and the interest rate is affordable.

Peer-to-Peer Lending

Another option is to borrow the money from an individual willing to lend it out of pocket in return for interest from you. There are a couple of peer-to-peer lending sites that facilitate these transactions and tend to have positive user reviews: Prosper.com and LendingClub.com are two to look into.

P2P lending sites like these are helpful because users (both investors and borrowers) are prescreened, while the interest rates charged tend to be more competitive than personal loan rates at traditional financial institutions. Both of these sites serve as the middlemen, matching investors with borrowers who meet qualifications, including a credit check. Like any other loan, the rate charged for a personal loan will depend on things like your credit score, amount borrowed and loan term. It's important to note that the maximum loan amount allowed by Prosper.com is $25,000, while LendingClub.com funds loans up to $35,000.

Why You Should Think Twice About Small Home Loans

Note that if you do manage to finance a home with a mortgage loan of less than $50k, the interest rate will most likely be higher to compensate for the money the lender is losing on the deal. Additionally, while closing costs of, say, $5,000 would be considered perfectly reasonable on a standard mortgage, that represents 10 percent of a $50,000 loan -- not so reasonable anymore.

So in answer to Sandy's challenge, the banks and rates available for mortgages under $50k vary by applicant, and you won't find them advertised. Some lenders outright do not provide these small mortgage loans, while those who will do so on a case-by-case basis.

I would advise anyone seeking a mortgage this small to stop for a moment and really think about whether it's worth it -- it might turn out that securing a mortgage loan for that little doesn't make sense financially. If you need a loan for less than $50k, consider finding an alternate of funding, maybe even borrowing from a family member or friend, or simply waiting on your purchase so you can save up the money you'd be spending on mortgage payments and pay cash instead.