7 year vs. 10 year mortgage: Check my math

[Grande]

I'm in the process of selling and repurchasing a new house. I currently have 8 years remaining on my 15 year mortgage. I expect to borrow about $105k. I am considering a 10 year 3.5% mortgage but am tempted by a 7 year 2.875%. I did the math and the difference in monthly payment in $343. At 7 years the 7 year mortgage is paid and full and equity is $105k where the 10 mortgage has a remaining balance of $35,454 (equity of $69,566). But I would have an extra $343/month to invest. It looks like to make up the difference of $35,454 I will need that $343/month to have a 7 year annualized return of just under 5.8%.

How's my math? Am I correct in this?   


Loan        Term  Rate      Mo Payment   Mo. Prin. Mo Int         Equity at 1 yr   Equity at 7 yrs   Total int @7yrs
105000   10   3.500   1038             732            306           8927                    69566           17562   
105000    7   2.875   1381             1130    252           13739            105000           11045   


Thanks.

[sokoloff]

Ignoring taxes, your math checks out.

https://docs.google.com/spreadsheets/d/1NsKrqBc1PE-5powxA44JeVfve3KSj4NLNRTgfBPBdyU/edit?usp=sharing

If flexibility is worth something to you, the 10 year and invest is also more flexible.

[Grande]

Ignoring taxes, your math checks out.

https://docs.google.com/spreadsheets/d/1NsKrqBc1PE-5powxA44JeVfve3KSj4NLNRTgfBPBdyU/edit?usp=sharing

If flexibility is worth something to you, the 10 year and invest is also more flexible.

Thanks for the reply. I am usually good with the math. It's just that the 5.8% comes as a surprise. Why is this?? It's essentially a guaranteed rate of return. An 5.8% isn't bad especially where equities are valued right now. Sure the 10 year has flexibility but my home equity relative to my other assets is low (under 15%) and I am putting myself on the 5 year plan. A paid off mortgage helps with things, cash flow in particular.

[nereo]

careful, your calculation conflates nominal annualized returns with real annualized returns to arrive at your 'guaranteed rate of return'.
As such and particularly over 7+ years your real returns are likely to be substantially less.

I tend to agree with sokoloff - at the rates you are considering i'd take the 10yr and its increased flexibility.

Also - what percentage of your NW will your home constitute if you follow these two paths?

[maizefolk]

It's just that the 5.8% comes as a surprise. Why is this??

Well it comes from a much smaller change in the interest interest rate on a much larger total balance.

Now what's interesting is what happens if you run the scenario at to the end of 10 years (so from the start of year 8, you put 1130 into the market in the 7 year mortgage scenario and continue to put in 343 in the other scenario).

At the end of 10 years, both houses are paid off, but (if we assume a 5.5% nominal annual return*), you end up with $54,318 in stock market investments in the 10 year mortgage scenario, but only 44,031 in the 7 year mortgage scenario.

In other words you come out $10,287 ahead with the 10 year mortgage after a decade, even though you're paying a higher interest rate than on the 7 year.

*Which would probably be something like 2-3% real returns given current inflation rates. This would mean it had been an extremely crummy decade for the stock market, but not great depression or 1970s bad.

[Grande]

careful, your calculation conflates nominal annualized returns with real annualized returns to arrive at your 'guaranteed rate of return'.
As such and particularly over 7+ years your real returns are likely to be substantially less.

I tend to agree with sokoloff - at the rates you are considering i'd take the 10yr and its increased flexibility.

Also - what percentage of your NW will your home constitute if you follow these two paths?

Home equity as a % of net worth won't be all that different from now (15-20% assuming house does not appreciate from today's value.). I put in about $4500/month to investments. This includes two maxed 401k/403b accounts, two Trad IRAs, and one HSA. I put the remainder in taxable accounts and presently a little bit to the principal of my mortgage. With current balance and assuming a fixed 4500/month at 5% return it's a projected $1.44M in 7 years.