PMI increases the effective annual rate. The longer it is paid, the more it increases the rate. The results are stated in Effective Annual Rates of Return and how the PMI impacts those rates. The effective annual rate takes into account the monthly compounding of mortgages. For example, an 8% annual rate becomes 8.3% when the monthly compounding is considered. PMI increases the effective annual rate. The longer it is paid, the more it increases the rate. |
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This calculation evaluates Private Mortgage Insurance in two ways. First, it evaluates how PMI changes the interest rate (Internal Rate of Return or IRR) of the mortgage. Second, it calculates the Present Value of the additional PMI premiums. This calculation assumes the following: •A fixed rate mortgage. •A mortgage with a term of 30 years. The PMI premium rates built into this program are for a thirty-year mortgage. •No points are charged on the mortgage. •No Closing Costs •Only principal, interest and PMI are considered. Escrow accounts for insurance, PMI and taxes are ignored. •Taxes are not considered. The emphasis is on comparing mortgages with and without PMI, as opposed to tax advantages. The default PMI rates are: •0.78%/12 X loan amount for 95% down & for first 20 Years •0.52%/12 X loan amount for 90% down & for first 20 Years •0.32%/12 X loan amount for 85% down & for first 20 Years •0.20%/12 X loan amount after 20 Years The above rates are from a business and economics paper Understanding the Cost of Private Mortgage Insurance by L. Lee Colquitt and V. Carlos Slawson. The paper is available at: http://www.westga.edu/~bquest/1997/costof.html The user may elect to override the default rates and type in his PMI monthly premium. In this case, the monthly PMI premium will be used for all months in the term of the mortgage. However, the logic that stops the PMI payment at 80% loan value will continue to work. That is, the results will include the IRR and PV for both: •Stopping the PMI at 80% Loan Value and; •Paying PMI for the life of the mortgage. Description of the Worksheet: Column one is the month of the mortgage. Column two is the balance at the beginning of the month. For the first month, it is the amount of the mortgage. For subsequent months, it is the mortgage principal balance at the end of the previous month (Column six). Column three is the monthly payment made each month. It only includes the principal and interest. It does NOT include escrow accounts for taxes and insurance. This payment can be calculated using the Time Value of Money financial function PAYMENT. Column four is the monthly interest. It is the monthly interest rate times the balance at the beginning of the month in column two. The monthly interest rate is the annual interest rate divided by 12. Column five is the principal amount paid each month. It is the monthly payment in column three less the monthly interest in column four. Column six is the balance at the end of the month. It is the balance at the beginning of the month less the principal paid each month in column five. Column seven is the monthly cash flow. Column eight contains the Monthly PMI Amount. Column nine is the monthly PMI payment. If you use the default rates (built into this calculation), this amount will change at 20 years (240 months). The default PMI rates are: •0.78%/12 X loan amount for 95% down & for first 20 Years •0.52%/12 X loan amount for 90% down & for first 20 Years •0.32%/12 X loan amount for 85% down & for first 20 Years •0.20%/12 X loan amount after first 20 Years of loan However, you can also enter your own PMI rate ($ per month). If you do so, that amount will be used for all months of the mortgage term (both before and after 20 years). Column ten is the cumulative PMI payments. It is simply the sum of the PMI payments for each month. Column eleven is the cash flow if PMI is paid until the mortgage balance is less than 80% of the original mortgage amount. Column twelve is the cash flow if PMI is paid for the life of the mortgage. Column thirteen is the present value of each PMI payment. That is, it converts the future PMI payments into today’s dollars (or buying power). It uses the Present Value financial function PV(rate,nper,pmt,fv,type) and the following inputs: Rate is the Client’s Investment Return converted to a monthly rate by dividing by 12. The number of periods (nper) is the number of years in the first column of the spreadsheet. Payment is zero. Future Value (fv) is the amount of PMI in column 8 of each row. Type is zero which means the end of the period (month). Column fourteen is the cumulative present value of PMI payments. It is simply the sum of the present value payments in column twelve. Column fifteen is the year of the mortgage. Effective Rate of Return: Annual Percentage Rate (APR) is converted to Annual Effective Rate (due to monthly compounding) using the following formula: •(1+ APR/12) ^12 -1 |