The Money Mustache Community
Learning, Sharing, and Teaching => Ask a Mustachian => Topic started by: Kierun on January 19, 2015, 02:46:59 PM

I’m having difficulties wrapping my head around the equations and formulas to determine the financial benefit, or lack thereof, of a theoretical use of lower rate loans to pay higher rate loans. So I'm hoping you mathmagicians can help out, thanks in advance.
Say you had a loan of 300k @ 5% and could repeatedly obtain 10k loans @ 3%. Would there be any financial benefit to take the 10k loan put immediately towards the 300k loan and once the 10k loan is paid off take another 10k loan to put towards the 300k loan, rinse repeat until 300k loan paid off? Trying to keep it simple, make whatever assumptions necessary to fill in missing variables. I’m interested in the math rather than the practicality and applicability.

Don't know about a closed form equation, but the numerical analysis is doable. Downloading this spreadsheet: http://office.microsoft.com/enus/templates/loanamortizationscheduleTC001019777.aspx will help.
You can add more details with Net Present Value (NPV) calculations, but we'll ignore those for this post.
First, pick the payback period for your $10K loan and calculate the interest cost for one such loan with the downloaded spreadsheet.
Then calculate the interest cost of the $300K loan (base case) with no prepayments.
Then, insert $10K prepayments into the $300K loan calculations at the appropriate times.
Calculate the total interest costs and compare to the base case.
You should also compare the interest reduction in the $300K loan if you simply apply the amounts going to the $10K loan to the $300K loan instead.
Does that make sense?

Sure, though you should make sure you account for the costs of taking out the loan... origination fees, that sort of thing.

Thanks MDM, you confirmed the calculation processes I imagined would be needed. Thanks Gimp for the reminder of origination fees and other related fees.

If you're in Hawaii, it sounds as if you discovered or heard of Sweep.

I heard about Sweep several years back, read through their website and then forgot about them. I had to google them just to jog my memory and remember anything about them. And will probably forget all about them again soon.