Let's take $100,000 as an example.
20% down is $20,000 and 10% down is $10,000
So on your first example, you owe $80,000x.05 (simple interest, not compound...and yes, I am aware that most mortgages are compound)
You want to calculate the interest on $80000 at 5% interest per year after 15 year(s).
The formula we'll use for this is the simple interest formula, or:
Where:
P is the principal amount, $80000.00.
r is the interest rate, 5% per year, or in decimal form, 5/100=0.05.
t is the time involved, 15....year(s) time periods.
So, t is 15....year time periods.
To find the simple interest, we multiply 80000 × 0.05 × 15 to get that:
The interest is: $60000.00
That's 60k you will have paid in interest alone, in addition to the 80k that you already owed, plus the down payment which is not included in the interest calculation, for a total of 160k you will have paid on a $100,000 home when the mortgage is amortized.
Example 2:
You want to calculate the interest on $80000 at 10% interest per year after 15 year(s).
The formula we'll use for this is the simple interest formula, or:
Where:
P is the principal amount, $80000.00.
r is the interest rate, 10% per year, or in decimal form, 10/100=0.1.
t is the time involved, 15....year(s) time periods.
So, t is 15....year time periods.
To find the simple interest, we multiply 80000 × 0.1 × 15 to get that:
The interest is: $120000.00
With interest and principle you will have paid $220,000 on a home.
I know this is confusing, but let's add another factor into the equation: Time, or, better put, inflation. Obviously if you're looking at real dollars, without knowing the rate of inflation, the first example is the most fiscally prudent. If we compare real dollars from 2000 (ten years ago) with real dollars from today, then you would have probably ended up paying more on the second example. It seems like the first example, 5%, would always be the best given the current status quo.
The only scenario that may change that is a depression or some situation where real dollars are significantly devalued. See the note in parenthesis below, and if I'm wrong, feel free to correct me because that is an interesting question.
(I'm sorry, I'm not an economist, but I am 1/8 Jewish, AND I did take macro and micro, albeit from an instructor who spoke Korean most of the time...I ended up learning everything from the book and skipping classes, and I did stay at a Holiday Inn Express last night as well)
First, alot more people than you think. Right now we have people walking away from mortgages who have the ability to pay merely because of what I mentioned before. Second and thirdly, I have a huge mistrust for the banking system right now and even the Fed. I'm sorry, you might think this is bullshit, but my 401K practically disappeared in 4 months. I didn't have much in it, but to watch it shrivel away was ridiculous. I had good investments, Vanguard mutual funds and acted on the advice of Suze Orman, the Goddess of all things financial, and I still got screwed royally.
My only remotely valid argument against your example is that I don't know anything paying 7% right now (CDs, savings, bonds, etc.). Assuming you could find a nice, juicy JG Wentworth style annuity such as from a settlement advance or certain types of trust funds and had all other financial liabilities squared away, having the monthly income pay the mortgage for you would definitely be a good idea. Call me paranoid, but again, I'm a firm believer in the mattress system at this point. My grandfather was moderately wealthy, lived during the Depression, and dealt with cash his entire life. It was only when some slick investment banker talked in into investing 800k into some shitty, SEC prosecuted company called HomeGold Investors that he lost that entire sum.
Clarifying, owning a home free and clear is never a volatile thing. Again, if you have the money, and can afford it (two separate things, but many do not know what the concept of affordable is...hence the current predicament in which we find ourselves) then buying something outright, whether it is a home or a consumer good (personalty) free and clear of any creditors is always a no brainer, a good decision like Samuel Adams beer.
I wish I would have stuck with business administration and finance in college. I couldn't take the material of the computer science/programming courses that my college, a highly ranked program per USN&WR, insisted that I take. My mind just isn't geared that way Otherwise I had a 3.25 in my major without even trying. I guess I should have transfered to a program where such courses would be elective and not required, but that's youthful inexperience for you.
Oh, and in closing, I leave ya'll with the following quote:
"Recent research has shown the empirical evidence for globalization of corporate innovation is very limited. And as a corollary, the market for technologies is shrinking. As a world leader, it is important for America to provide systematic research grants for our scientists. I believe strongly there will always be a need for us to have a well-articulated innovation policy with emphasis on human resource development. Thank You."
*blacks out*