Refinance or not. Math inside

[Neva6]

Need some other opinions on if I should refinance down to a 15y mortgage.

Current mortgage closed last year
rate 4.375%
term 30 yr
balance $242000
payment $1212 

New mortgage - No Closing Cost
rate 3.25%
term 15 yr
payment $1704 

Essentially $500 a month more would net me interest savings starting at $230/month for a combined additional $730 towards principle each month. 

Scenario A -
Switch to 15y. At end of 15 years, all 242000 paid off. No additional investing.

Scenario B -
Stay with 30 year. At end of 15 years $90800 of principle paid down. IF I invested the extra $500 a month I would need a 7.3% return to get a value of 151700, which when added to the principle equals the same value as Scenario A of $242000. 

Is scenario A the same as getting a 7.3% return on the $500? Is this a weird way to think about this?

At the end of the month I have $1000 extra for future cars, vacations, investing, OR this additional $500. I am investing about $1300/month for retirement. No other debts.

What would you do?

[gluskap]

Our numbers are slightly different but we chose to refinance to a 15 year. I know a lot of threads say you will have more money investing the difference instead of prepaying a mortgage but I'd rather take the guaranteed return. I think refinancing forces you to actually put the money into your equity versus you actually having the discipline to invest the money. Also I think when you retire makes a big difference as well. If you are on track to retire in 15 years then it makes more sense to refinance since with a paid off house you can reduce your expenses in retirement which would be better for taxes. I think with the rate reduction from refinancing you would save money on interest so it seems worth it.

[MDM]

It's somewhat of an apples vs. oranges comparison, so the answer to "Is scenario A the same as getting a 7.3% return on the $500?" is "no."

Take a slightly different example, where one invests $100 in A that returns 10% for 6 years, vs. investing $105 in B that returns 11% for 6 years:

A: $100 invested, $177.16 returned
B: $105 invested, $196.39 returned

With B, $5 more was invested and $19.23 more was returned.  That does not mean the extra $5 returned 25.2%.  Do you see where your A vs. B comparison is similar?

Compare a 30 year mortgage vs. a 15 year mortgage, both with the same interest rate, and the extra money available with the 30 year mortgage will need to be invested at...exactly the same rate as the mortgage rate...to be able to pay the principal after 15 years.

Your larger question of "which option is better?", however, seems well calculated.  Going to the lower interest rate on the entire principal means you need something much better than the 4.375% on the relatively small amount you can invest by keeping the lower monthly payments.

[Bob W]

Be interested in how you get no closing costs?   Is someone lying to you?  This shit generally ain't free.

[Neva6]

Thanks MDM for your explanation.

For no closing cost my rate is 3.25%. If I paid the costs the rate would be 3.0%.