Saving for a Down Payment

So what about down payments?  Last time I said that they either came out even or that they worked out better for you when interest rates were higher.  That's because there are two kinds of assumptions that I can make when analyzing them.

My goal in comparing high to low mortgage rates is that I am trying to hold all the other factors that you can control equal.  One factor that you can't control is how much someone else is willing to bid for the house, which means that lower interest rates will mean higher house prices.  Another factor you cannot control is the down payment required by the bank.

Usually down payments are measured as percentages of house prices.  Currently in Canada you need a down payment of at least 5% but the higher the down payment the better off you are in terms of insuring your mortgage.  We'll use the same numbers as last time - 25-year amortization period, 300 currants a month to spend on mortgages - and then consider once again the 3% interest vs. the 12% interest scenarios.  Add to this a requirement of a 5% down payment.

In order to make that down payment you'll have to save money.  While you are saving money you are going to have to pay rent.  Let's say that while renting you manage to set aside 50 currants a month to save for a down payment.  If the bank is charging 3% interest for a mortgage, they surely aren't paying out very much at all.  They probably pay you something around 2 percentage points less.  That means at a 3% mortgage rate (so a 1% interest rate on your own investments) you will have saved up for a down payment after 62 months.  That's just over five years.

If the banks were charging 12% for a mortgage and paying out 10% then you would need to save for only 27 months, two and a quarter years, before you had 5% of the value of your home.

The huge difference is because of the different cost of the house.  With a cost of 63.5k you would need to save up more than twice as much as you would with a cost of 29.8k.  It also matters that you are earning more interest.  With 12% mortgage rates by the end of the second year you've earned 21% interest on the money you deposited during the first month.  Since you're deposting only 50 currants that's only 10, but it's something.

With a 3% mortgage rate after two years you've only earned 2% interest on the initial deposit.  You've earned a mere 5% interest on the initial deposit after the full five years.  The thing about 1% interest rates is that it takes a long time before you even notice the compounding.  In fact, because the amount of interest paid is rounded, it is possible that it doesn't compound at all over such a short number of years.

Basically you need to save up much longer to afford a down payment on your home purchase when interest rates are lower.  The down payment required is higher and you earn less interest while you are saving.

Now I mentioned that there is another way to look at this where there is basically no difference between the two rates.  And that is to say that if two people both had equal opportunity to save up a down payment ahead of time then they will have down payments of equal size which will essentially add to the maximum loan they are allowed to take out to determine the price of the home.  That is, if we assume that people have five years to save up a down payment then under the higher interest rate everyone will have a higher down payment available, which will mean everyone will need that down payment to compete with one another.

This uses the same competitor-is-probably-in-the-same-boat-as-you methodology I used yesterday.  In this case, though, it ignores the fact that you and whoever is competing with you for the house are both in the same boat - you both have to delay your decision to buy a home for an amount of time it takes to save up a down payment.  Even if the interest rate doesn't affect your ability to compete for the house you want, it still might mean you'll be bidding on a house you want years later.

One possible argument is that because low interest rates make it harder to save up a down payment they will also lower the price of houses.  After all, if the bank demands a 5% down payment then only those people who can afford such a down payment can bid.  So in addition to being capped by the income of the people who are interested in buying, the value of a home is capped at 20 times the down payment available to the people buying.

There may be some merit to this argument.  With lower interest rates it is harder to save up large chunks of money, so people are less likely to have large down payments, which means that housing prices might be capped by down payment size rather than income size.  Personally I don't think this reflects the reality of the current housing market.  When 40-year amortizations were allowed people took advantage of them, which shows that people are willing to make a house much more than a 25-year investment.  That means that saving up for five years to afford a down payment might be well within what people are wiling to do.  I also don't think it is a coincidence that low down payment requirements have come hand-in-hand with lower interest rates.

Of course once we start talking about the reality of the housing market our entire simple model falls apart - and even if low interest rates and low down payments occurred as part of the same policy, that doesn't mean there couldn't be a different policy in the future.  I can't deny the possibility that under some sets of circumstances down payment size would be more of a limiting factor on mortgages than income, especially if rental prices are very high so people who aren't buying have trouble saving.  And obviously if a down payment of 10%, 15% or 20% were required then the size of down payments might be severely limiting.  As an exercise, you could brainstorm other factors that might contribute housing prices being limited by the size of the down payments that buyers can afford!

I still want to construct some scenarios about the market going up and down and "building a nestegg" by paying down your mortgage, so I'll probably keep talking about mortgages for at least another post,

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