### Author Topic: Could someone double check my math?  (Read 3345 times)

• Bristles
• Posts: 368
##### Could someone double check my math?
« on: July 15, 2012, 11:51:23 AM »
This just isn't making sense to me. Could not paying down the mortgage be a better option?

Scenario 1:

Home purchase \$218,750, 20% down (\$43750) All closing costs to be paid by seller, loan of \$175K on 30 year mortgage @ 3.5% interest, payments of \$785 month

Pay just the \$785 month for 16 years until retirement(\$150,720 in total payments). Save \$415 a month until retirement=\$79,680 saved plus any interest at retirement. Loan balance of \$104K at retirement.

Sell the home for \$275K net after realtor and other fees, pay off the \$104K mortgage balance leaving \$171K.

Since we will have paid in \$151K in payments and \$44K in the down payment, but saved \$80K during that time, that leaves this scenario at a gain of \$56K.

Scenario #2:

Home purchase \$218,750, 20% down (\$43750) All closing costs to be paid by seller, loan of \$175K on 30 year mortgage @ 3.5% interest, payments of \$785 month

Pay the \$785 plus \$415 a month for 16 years until retirement(\$227K total payments, PIF 3 months before retirement), save \$3300 in those last couple months before retirement

Sell the home for \$275K net after realtor and other fees.

Since we will have paid in \$227K in regular payments plus \$44K for the down payment and saved \$3K during that time, this scenario is a gain of only \$7K.

Is my math right? It doesn't seem logical that not paying off the mortgage would be a better option. We only plan to be in this home for the bulk of our child raising years and then downsizing to a very small home at retirement so paying it off would only be for a financial advantage at the time of switching homes. Our retirement home will be paid in full when we move. Also, these figures don't represent our regular retirement savings, just the portion for a housing allowance and what would be the better way to go as far as making payments/saving.

TIA!

• Walrus Stache
• Posts: 5185
##### Re: Could someone double check my math?
« Reply #1 on: July 15, 2012, 03:49:35 PM »
First, it looks like your selling estimate after 16 years is reasonable - a \$300,000 selling price less a 6 percent commission and some selling expenses would net you around \$275,000.  That would mean around a 2 percent compound annual increase in the value of the house.

Here's how I would look at your two scenarios.

Scenario 1

You pay OUT \$44k in the down payment, \$151k in principal and interest payments, and \$80,000 to your savings account, for a total outflow of \$275,000.  At the end of the 16 years, you get BACK \$171,000 in net house equity plus your savings of \$80,000 (ignoring interest), for a total of \$251,000.  You lost money.

Scenario 2

You pay OUT \$44k in the down payment, \$227k in principal and interest, and \$3,600 to your savings account (3 x \$1,200).  The total out is \$274,600.  At the end of 16 years, you get BACK \$275,000 in house equity and \$3,600 in savings (ignoring interest), for a total of \$278,600.  You are slightly ahead.

I think you have incorporated a sign error in thinking about the amount in the savings account.  Your cash flows to the savings account are going OUT of your pocket and into the bank account.  The money comes BACK to you at the end of the 16 years, just like the equity in the house does.  Does this make sense now?

#### TLV

• Bristles
• Posts: 492
• Age: 32
• Location: Bellevue, WA
##### Re: Could someone double check my math?
« Reply #2 on: July 15, 2012, 04:07:07 PM »
Another Reader has it right - you're double-counting the 80k saved in the don't-pay-it-down scenario. As described, you'd be ahead about 30,000 by paying it down.

That said, if you can earn more on your investments than the 3.5% mortgage interest rate over the 16 years (in other words, more than the ~\$30,000 difference), you might still be better off by investing the extra money elsewhere instead of paying down the mortgage.

#### gooki

• Handlebar Stache
• Posts: 2412
• Location: NZ
##### Re: Could someone double check my math?
« Reply #3 on: July 15, 2012, 04:38:12 PM »
Just to add, if your time frame is 16 years, do the maths on a 15 year mortgage at sub 3% interest.

#### Lars

• Stubble
• Posts: 105
##### Re: Could someone double check my math?
« Reply #4 on: July 15, 2012, 04:49:39 PM »
You beat me to it gooki. With a rate of 3% on a 15 year mortgage, you would be looking at the same payment as option 2 which would saving you nearly \$11000 in interest. Get a rate of 2.75% and you are rewarded with \$14,500 interest savings and a lower payment for committing to the shorter payment schedule.

• Bristles
• Posts: 368
##### Re: Could someone double check my math?
« Reply #5 on: July 15, 2012, 06:00:20 PM »
Thank you folks! Yes, that totally makes more sense now. I was not adding in the savings funding as an outlay and was just counting it coming in.
I did check out the possibility of a 15 year mortgage but we prefer the flexibility of having extra money for investing, whether that's in an aggressive pay-off strategy or for other investment items.

So the math should go:
#1
\$44K down, \$175K mortgage, \$785 mo x 16 years on the mortgage and saving \$415 mo leaves a balance on the mortgage of \$104K at retirement and a savings account of \$80K(+ \$6.5K at a 1% interest)
My outlay is \$44K + \$151K + \$80K=\$275K
Sell and net \$275K-\$275K outlay= even(or +\$6.5K at pathetic interest)
#2
\$44K down, \$175K mortgage, \$785 mo + \$415 extra mo x 16 years on the mortgage leaves the mortgage paid off and a savings account of \$3300(it's a smidge less than 3 months)
My outlay is \$44K, \$227K, \$3K= \$274K
Sell and net \$275K-\$274K= \$1K ahead of no interest in Scenario #1 or \$5.5K less than with interest in Scenario #1

???

Doesn't seem to be very much difference. Overall I'm leaning toward not paying it down and using the extra money for a income property or two.

• Walrus Stache
• Posts: 5185
##### Re: Could someone double check my math?
« Reply #6 on: July 15, 2012, 06:41:40 PM »
No.  Your net under Scenario 1 is the \$171,000 you get back from the sale of the house and the \$80,000 that you get from the savings account, or \$251,000.  You have lost \$24,000.

Your house is appreciating at 2 percent but the mortgage is costing you 3.5 percent.  This is called negative leverage and is why you are losing money.  Make sense?

Note the value of the tax deduction for the mortgage interest and the explicit discounting of cash flows to account for the time value of money are not considered in this calculation.