## Mortgage Calculation Helper

#### Mortgage Rates are at Historic Lows

posted Nov 15, 2011, 11:04 AM by Bert Bingley

 It is time to refinance.

posted Dec 1, 2009, 7:38 AM by Bert Bingley

#### Calculating Mortgage Costs (w/ Equations!)

posted Nov 11, 2009, 6:00 AM by Bert Bingley   [ updated Nov 11, 2009, 4:17 PM ]

There are many variables that contribute to calculating the future cost of owning a home.  In this article, I outline the variables involved and write out the equations used to calculate the total cost.

For most home purchases, there are two periods that need to be considered.  In the first period, the home owner has to make monthly mortgage payments.  Once the mortgage is completely paid off, the home owner enters the second period where mortgage payments no longer have to be made.

 Buying Variables Assumptions Selling Variables Mortgage Term (years) Home Appreciation Cost of Sale (%) Points Investment Appreciation Years Owned Interest Rate Tax Rate Down Payment (%) Rent Appreciation Purchase Price Home Insurance Closing Costs Annual Rental income

Next, let's enumerate the nominal cost associated with owning a home.  By nominal, I mean the actual cost paid out of pocket.  To generate the opportunity cost adjusted total cost, or, the real total cost, we will have to incorporate the rate of return on alternative investments, .  For now, let's just look at the nominal costs:

 Buying Costs Annual Costs Selling Costs Mortgage Points Mortgage Payment Cost of Sale Closing Costs Taxes Principle Due Down Payment Insurance Cash from Sale Rent

In the table above, the variables , and  represent the sum of the buying costs, annual costs, and selling costs, respectively.  Finally, to determine the real cost, we have to adjust each of these cost to account for the opportunity cost of money.

Putting it all together, the equation for total mortgage/home cost when  is

When the , the mortage will have been totally paid off.  To recomupte, we must subtract the mortgage payment for the period after .  So for this situation, we have the following mortgage/home cost equation,

In forthcoming posts, I will analyze these equations to show which terms dominate the costs in the long term.  Another plan I have is to show the break even trade space in terms of home appreciation, investment return and rental income.  Stay tuned....

bert@mortgagecalculationhelper.com

#### Mortgage Costs

posted Sep 16, 2009, 6:56 AM by Bert Bingley   [ updated Sep 19, 2009, 8:40 AM ]

 When shopping for mortgages, the obvious question is: which set of mortgage options will cost me the least?  This turns out to be a fairly complicated question to answer.  The difficultly in giving a concrete answers rests in the fact the certain assumptions have to be made in order to calculate long-run mortgage/housing cost. Below, I list the important variables involved in calculating mortgage/housing costs.  The variables in bold are not known a priori when one buys a house, and the parenthetical values are the values assumed for our analysis.Known VariablesClosing Cost (4% of purchase price)Home Insurance Rate (0.46% of home value)Tax Rate (1.35% of home value)Cost of Sale (6% of selling price)Mortgage TermPoints (0% of mortgage loan)Interest Rate (4.8%)Down Payment Purchase Price (\$100,000)Unknown VariablesHome AppreciationInvestment Appreciation    So, the process for calculating future value cost of owning a home (financed with a mortgage), is simply a function of all of these variables. Fortunately many of the variables are known (to a large degree). However, two variables must be estimated in order to calculate costs: the rate at which the purchase property will appreciate and the rate at which any other investment assets will appreciate (return on investment; ROI).     As an estimate for ROI consider that the average ROI on US stocks over long periods of time varies from 8%-12%. On the other hand, house appreciation has only sustained an approximately 3% return over long periods of time. There are notable exceptions like high-demand urban areas where home appreciation approaches 8%. Interestingly, as we will show in a subsequent post, the choice of mortgage is completely independent of the house appreciation rate, but is highly dependent to the non-home ROI.    Below are several plots for various ROIs and mortgage options. Two general conclusions can be drawn from these plots:When the ROI (i.e. the opportunuity cost of money sunk in a house) is high, You want to keep as much money as possible and put as little into paying off your house as possible.When the ROI on alternative investments is low, it also makes sense to pay off your home as quickly as possible.    By high ROI, we mean and ROI that exceeds the mortgage rate. The plots show, that for high ROI, even after the short-term mortgage has been paid off, the opportunity cost of having all that capital sunk in a house far out paces the cost of additional payment. bert@mortgagecalculationhelper.com

#### Mortgage Considerations

posted Aug 22, 2009, 3:14 PM by Bert Bingley   [ updated Aug 22, 2009, 3:53 PM ]