A consideration of mortgages

When work becomes a bit dry, I let my brain wander onto other things... two weeks ago it was bicycles and monorails. Today: It might be that time in life for some of us (maybe not for you grad students) to consider buying a house and settling down. Natural questions arise, such as, "how much can I afford on my current salary?" and "how long should I take to pay it back?" Mortgage "calculators" offered by banks such as TD are often oversimplifying the problem, and only shed light on the relationship between monthly payment, principle, interest rate and payment term. There are far more factors involved than just those. Anyone who tells you "every dollar you pay in rent is money thrown down a well" is either a loan officer, a real estate agent, or an miseducated (but well-intentioned) parent; none speaks the truth. If you're planning on buying a house in a few years, rent you're paying now is buying you time to save up for a big enough down payment to save on interest from a mortgage. Provided you have a job. Let's say you're currently renting and can put $20k into a savings account each year. And let's say you plan on one day taking up a 15 year mortgage at 10%. It might occur to you that for each additional $20k (a single year's savings) you put into a down payment, you will save $63.5k in interest by the end of your 15 year term (because you didn't have to borrow an extra $20k for 15 years at 10%). Suddenly that $500 a month rent seems worth it, right? Even that's oversimplifying it. Your savings is generating interest of its own at 4% (or if you're smart and have a good investment, 9%). The type of house you want to buy is perhaps growing in price at 5% a year. Maybe your rent is actually zero because you live with your parents. For each additional $20k you put into a down payment, your payment term decreases (for the same monthly payment), which decreases the savings on interest caused by the next 20k you put in. So bottom line: when's the best time to buy that house? Finding no easy answer on the internet (or maybe I didn't look hard enough), I set out to answer that question on my own. I haven't quite worked out the kinks in my formula yet, and this post is getting too big, so stay tuned for the conclusion.