The Calculus Diaries - Jennifer Ouellette [52]
Option 3: This is a two-bedroom, two-bath unit with den in a prime location with excellent walkability. The design features Mediterranean influences, with a balcony, spacious living room and open kitchen, and luxurious baths. The price per square foot is significantly higher, so we can only afford one of the smaller units. There are fewer closets, and the parking spaces in the shared garage are tandem.
All else being equal, how do we find the optimal choice among them? Calculus is less helpful here. Ultimately, one’s choice of home is an emotional, subjective decision. But we do engage in an approximation of an optimization problem whenever we comparison shop; it’s one way to bring some rationality to the process. Yet even then, our choice of how much to weight a given variable is highly subjective. Dutch psychologist Ap Dijksterhuis studies how house hunters are often subject to “weighting mistakes.” Given the choice between a larger home in the suburbs with a longer commute, and a smaller, more expensive home in a central location, most home buyers opt for the larger home. They underestimate the negative impact of a long commute on overall quality of life over time.
DOWN THE RABBIT HOLE
In the end, we choose Option 1. We trade our former prime downtown location for extra space, a shorter commute for Sean, and a private garage. Now the nail-biting anxiety sets in as we try to lock in our mortgage rate. The rates change literally every day. Two days after our offer is accepted, we get a nasty surprise: There is a new 1 percent hike in mortgage interest rates for condominium units. So that 5.25 percent interest rate we used to calculate our estimated monthly payments will be 6.25 percent instead.
The earliest recorded mortgages date back to 1190 in England, when landowners would sell their land for a set fee, with no interest. Whatever the land produced would enable the buyer to pay the seller. Mort comes from the Latin word for “death,” while gage means a pledge to forfeit an asset for nonpayment of a debt. The modern concept is not much different: We want to buy a house, but we don’t have enough cash in hand to pay the full price, so we put down the cash we have and borrow the rest, using the house as collateral. There is a monthly payment, determined by the interest rate (usually fixed) and the lifetime of the loan (typically thirty years). At the end of that time, we will have paid off the principal loan plus the accumulated interest.
It’s instructive to crunch the numbers and see firsthand why a mere 1 percent hike in the interest rate makes a significant difference on one’s monthly payments. Let’s round down the respective rates to 5 percent and 6 percent to make our calculations easier. If we took out a modest $100,000 mortgage at 5 percent, our payment would be $536.82 per month, compared to a $599.55 monthly payment at 6 percent interest. This assumes the interest is charged yearly. According to Mark Chu-Carroll, a computer scientist who blogs at Good Math, Bad Math, even this trivial difference can result in a higher monthly payment. We would only pay $525 per month at the 5 percent rate if the interest were calculated monthly. Just an extra $62 per month over 30 years adds up to roughly $22,320 in additional interest.
Fortunately, our story has a happy ending: We are able to negotiate our original estimated interest rate with one lender. It helped that we had a sufficient down payment. Early in the 1900s, aspiring homeowners in the United States were required to have a 50 percent down payment on a five-year mortgage. Because very few people could meet those conditions, fewer than 40 percent of the population owned their own homes, compared to nearly 70 percent today, when 20 percent down is more common for a thirty-year mortgage. How long would it take to save 20 percent of a $300,000 home? That is $60,000—not an easy sum to accrue on a standard living wage. But it is a simple matter to figure out how much