HOW TO CALCULATE THE SAVINGS BY NOT PAYING DOWN YOUR MORTGAGE (using the previous post as an example)
B = Mortgage balance [$160,000]
P = Mortgage payment (should be principle and interest only, exclude property taxes, property insurance, PMI, or anything else in escrow) [1,645]
N = number of payments remaining [120 = 10 x 12]
IM = EFFECTIVE Interest rate on your mortgage [.0433]
II = Interest rate on investments [Assuming .07 per year]
Calculate M= Monthly Investment Interest rate = (1+II)^(1/12) = 1.07^.0833333 = 1.0056541
If you don't know P, you can either go to a calculator on the internet or in Excel Type in =-PMT(0.0433/12,120,160000) to get the answer.
Deciding between a payoff assumes you have $160,000 lying around to extinguish the mortgage. The question is what is the difference at the end of 10 years between:
1) Leaving the $160,000 invested and regular making mortgage payments.
2) Paying off the $160,000 and immediately investing the newfound $1,645 each month at the investment rate.
Option 1 is easy to calculate. At the end of 10 years you have 160,000 x 1.07^10 = $314,744.
Option 2 is more convoluted. The first $1,645 payment grows by 1.07^10. The second $1,645 payment grows by 1.07^9.917, etc. The total is $282,973.
Here's how you calculate it: P x M x (M^N - 1) / (M - 1)
= 1,645 x 1.0056541 x (1.0056541^120 - 1) / (1.0056541 - 1)
= 1,654.30 x (1.96714 - 1) / 0.0056541
= 1,654.30 x 0.96714 / 0.0056541 (bit of rounding error)
The difference here is $31,771. Lower than other people's situations because (1) it's only a ten year mortgage, and (2) the interest rate is closer to 7% than many other people's mortgages. But for some people that could be easily be a year's worth of expenses, so prepaying your mortgage could delay your FIRE date by a year in this instance.
One other thing you should take into account is the effective interest rate of your mortgage. For those of us in the US that can deduct the interest rate on our mortgages (not everyone necessarily gets a benefit from this, you should check), that interest probably lowers your state and federal taxes. This calculation isn't so simple because we automatically qualify for a standard deduction, so if you aren't already filing a Schedule A you might not see a full benefit.
Hope that helps. If you can't be bothered to do the calculation, post your information here and I will try to help. People with (1) longer mortgages and (2) lower interest rates and going to find more benefit in not paying down early. I did this calculation for someone else on the forum and the difference was nearly TWO HUNDRED THOUSAND DOLLARS!
7% is the investment figure MMM has thrown around on the site, but you are welcome to tweak it depending on your age and risk tolerance. Any mustachian this involved in making their finances go longer sooner owes it to themselves to do this calculation before paying down their mortgage.