- For an investment of $3,200 in one year's time ($3,000 in principal payments and $200 appraisal fee), we would avoid $3,900 in PMI over a period of five years (January 2015 to February 2019); this is a 111% total return, 22.2% annualized. Not bad.

January of 2015 – February of 2019 is only four years and one month, not five years. Thus, you are able to snowball only 49 payments, not 60, reducing PMI by $2,937.55, not $3,900. That might sound like a bad deal (paying $3,200 to eliminate $2,900), but the PMI payments are not your only return. You will also save at least $3,000 in future payments realized at the end of your mortgage. To find, approximately, how much you will save at that time compute 3000*(1+.035/12)^n where n is the number of months between when you pay $3,000 to principle and the end of your mortgage based on the size of your future payments (an exact formula for Excel would be: =ROUNDDOWN(NPER(.035/12, payment, -3000*(1+.035/12)^months), 0)*payment-FV(0.035/12, ROUNDDOWN(NPER(0.035/12, payment, -3000*(1+0.035/12)^months), 0), -payment, 3000*(1+.035/12)^months)*(1+0.035/12) where payment is your future payment amount and months is the number of months until you pay off the mortgage with the $3,000 principle payment in 2015). Your annualized effective internal rate of return can then be computed using guess and check (or a financial calculator or Excel). The internal rate of return on the $3,200 will exceed the annualized effective rate on the loan, 3.557%.

However, you are snowballing your PMI payments into your mortgage, so your overall profit will be even bigger than above but realized entirely at the end of your mortgage. Consequently, your annualized effective internal rate of return will be lower than as is implied by the calculations in the last paragraph, perhaps significantly so. This is because the PMI payments are rolled into the mortgage earning 3.5% nominal annual return compounded monthly for the period of time between their occurrence and the end of the mortgage. Since 3.5% nominal annual return is less than the initial interest on the principle payment, the internal rate of return will be lower than above. However, your profit will be bigger because the payments to principle will further reduce the overall amount of interest paid on the mortgage. Less interest paid means fewer payments or a smaller last payment at the end of the mortgage.

As nawhite pointed out, the marginal return on money put towards principle later in the life of the PMI will be larger than money contributed sooner. However, the money contributed sooner has a longer period over which to compound, making the later payments worth less than the sooner payments in the broader context of the entire loan. In the example of 9.5% interest when $11,900 is owed versus 17.9% interest when only $5,000 is owed, paying off the $11,900 will take more than twice as long as paying off the $5,000 at the same payment level and interest rate. So, as $1 is worth $1.20 at the end of two years at 9.5% interest whereas $1 is only worth $1.18 at the end of one year at 17.9% interest, the earlier payment is actually worth more despite what you might conclude from looking only at the marginal rates as quoted above. Remember, money has a time value. It is not always correct to directly compare money or interest rates from different times.

BTW, it looks like you applied the formula r = R/t where R is the rate of return over the entire period, t is the time in years (you seem to have used 5 years), and r is the annualized return. That formula is for investments where you invest a certain amount, wait for a while, then profit all at once at the end of the time period. You cannot apply that here for two reasons. First, the PMI payments that you’re avoiding occur in small monthly installments over five years instead of all at once. Second, the time period is much longer than five years since you will not realize the profit until the end of your mortgage unless you plan on using the marginal equity for a loan between the time the marginal equity is realized and the time that it would have been realize if not for the $3,000 payment to principle and $200 reappraisal. In short, this formula is not valid in this situation.