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HUD   >   Program Offices   >   Housing   >   Comp   >   Premiums   >   Monthly (Periodic) Mortgage Insurance Premium Calculation
Monthly (Periodic) Mortgage Insurance Premium Calculation

The formula for calculating monthly mortgage insurance premium became effective May 1, 1998 (see Mortgagee Letter 98-22 Attachment).

Below is the monthly mortgage insurance premium (MIP) calculation with examples and pseudocode using the annual and upfront MIP rates in effect for mortgages assigned an FHA case number before October 4, 2010. See the following Mortgagee Letters for subsequent changes to the annual and upfront MIP rates: 10-28, 11-10, 11-35, 12-04, and 13-04 [PDF].

Premium Calculation

Monthly MIP Computation Steps Example
Step 1: Compute annual average outstanding balance (see below)  Average Outstanding Balance for 1st amortization year: $106,160.654166666666
Step 2: Average Outstanding Balance * Annual MIP Rate 

(round to 2nd decimal place based on value in 3rd decimal place).

106,160.654166666666 x.005 = 
    530.803270833333333
round to 530.80
Step 3: If MIP financed, divide annual MIP from Step 2 by (1 + Upfront MIP factor) 

Result rounded to 2nd decimal place based on value in 3rd decimal place.

530.80/ (1 + 0.0225) = 519.1198 

round to 519.12

Step 4: Divide by 12 and round to nearest cent for Monthly MIP. 

Result rounded to 2nd decimal place based on value in 3rd decimal place.

519.12/ 12 = 43.26 

round to 43.26

Step 5: Multiply by 12. 

This is the Annual Premium.

$519.12

Computation of Annual Average Outstanding Balance

To start, use the original loan amount as the previous balance. Repeat the following steps for the remaining months in the year (11 iterations). The calculation of subsequent years is the same. The second year will begin with the last result of the first year.

  1. Multiply previous balance times annual contract interest rate. Round the result to two (2) decimal places based on value in 3rd decimal place.

  2. Divide result by 1200. Round the result to two (2) decimal places based on the value in 3rd decimal place.

  3. Add previous balance.

  4. Subtract P&I payment. Note: For an ARM use original Interest Rate and original P&I through all years. For GEM/GPM compute current P&I based on amortization plan. See table below.

When the final year is computed, total up the 12 results for that year and divide the total by 12.

AMPLAN RATE OF INCREASE MONTHS OF INCREASE
A
.025
60
B
.050
60
C
.075
60
D
.020
120
E
.030
120
F
.049
120
L
.010
999
M
.020
999
N
.030
999
O
.040
999
P
.050
999

The new monthly P&I for GEM/GPM is not calculated if the twelfth month of the case has not been reached or if the payment number is greater than the maximum number of months.


Premium Calculation Example

Field Value
Original Mortgage Amount $106,605 
Interest Rate 7.5 
Monthly P&I 745.40 
Annual MIP Rate 0.005 
Upfront Factor 0.0225
Beginning Amortization Date 04/2008 
Today's Date 12/2009

Compute the annual average outstanding balance:

Month/Year Computation Result
Year 1 / Month 1  (Use Original Mortgage Amount) $106,605.00 
Year 1 / Month 2 
  1. 106,605.00 * 7.5 = 799,537.5000 (round to 799,537.50) 
  2. 799,537.50 / 1200 = 666.28125 (round to 666.28) 
  3. 666.28 + 106,605.00 = 107,271.28 
  4. 107,271.28 - 745.40 = 106,525.88 
$106,525.88 
Year 1 / Month 3 
  1. 106,525.88 * 7.5 = 798,944.1000 (round to 798,944.10) 
  2. 798,944.10 / 1200 = 665.78675 (round to 665.79) 
  3. 665.79 + 106,525.88 = 107,191.67 
  4. 107,191.67 - 745.40 = 106,446.27 
$106,446.27 
Year 1 / Month 4 
  1. 106,446.27 * 7.5 = 798,347.025 (round to 798,347.03) 
  2. 798,347.03 / 1200 = 665.2891916 (round to 665.29) 
  3. 665.29 + 106,446.27 = 107,111.56 
  4. 107,111.56 - 745.40 = 106,366.16 
$106,366.16 
Year 1 / Month 5 
  1. 106,366.16 * 7.5 = 797,746.20 (round to 797,746.20) 
  2. 797,746.20 / 1200 = 664.7885 (round to 664.79) 
  3. 664.79 + 106,366.16 = 107,030.95 
  4. 107,030.95 - 745.40 = 106,285.55 
$106,285.55 
Year 1 / Month 6 
  1. 106,285.55 * 7.5 = 797,141.625 (round to 797,141.63) 
  2. 797,141.63 / 1200 = 664.2847 (round to 664.28) 
  3. 664.28 + 106,285.55 = 106,949.83 
  4. 106,949.83 - 745.40 = 106,204.43 
$106,204.43 
Year 1 / Month 7 
  1. 106,204.43 * 7.5 = 796,533.225 (round to 796,533.23) 
  2. 796,533.23 / 1200 = 663.77769 (round to 663.78) 
  3. 663.78 + 106,204.43 = 106,868.21 
  4. 106,868.21 - 745.40 = 106,122.81 
$106,122.81 
Year 1 / Month 8 
  1. 106,122.81 * 7.5 = 795,921.075 (round to 795,921.08) 
  2. 795,921.08/ 1200 = 663.2675666 (round to 663.27) 
  3. 663.267+ 106,122.81 = 106,786.08 
  4. 106,786.08 - 745.40 = 106,040.68 
$106,040.68 
Year 1 / Month 9 
  1. 106,040.68 * 7.5 = 795,305.10 (round to 795,305.10) 
  2. 795,305.10 / 1200 = 662.75425 (round to 662.75) 
  3. 662.75 + 106,040.68 = 106,703.43 
  4. 106,703.43 - 745.40 = 105,958.03 
$105,958.03 
Year 1 / Month 10 
  1. 105,958.03 * 7.5 = 794,685.225 (round to 794,685.23) 
  2. 794,685.23 / 1200 = 662.2376916 (round to 662.24) 
  3. 662.234+ 105,958.03 = 106,620.27 
  4. 106,620.27 - 745.40 = 105,874.87 
$105,874.87 
Year 1 / Month 11 
  1. 105,874.87 * 7.5 = 794,061.525 (round to 794,061.53) 
  2. 794,061.53 / 1200 = 661.7179416 (round to 661.72) 
  3. 661.72 + 105,874.87 = 106,536.59 
  4. 106,536.59 - 745.40 = 105,791.19 
$105,791.19 
Year 1 / Month 12 
  1. 105,791.19 * 7.5 = 793,433.925(round to 793,433.93) 
  2. 793,433.93 / 1200 = 661.19494 (round to 661.19)
  3. 661.19 + 105,791.19 = 106,452.38 
  4. 106,452.38 - 745.40 = 105,706.98 
$105,706.98 

 

Total of the Year 1 results  $1,273,927.85 
Divided by 12
This is the Annual Average Outstanding Balance
$106,160.654166666666 

See Premium Calculation table at beginning of page for remaining steps to calculate Year 1 premium

 

Year 2 / Month 1 
  1. 105,706.98 * 7.5 = 792,802.3500
  2. 792,802.35 / 1200 = 660.668625
  3. 660.67 + 105,706.98 = 106,367.65
  4. 106,367.65 - 745.40 = 105,622.25 
$105,622.25 
Year 2 / Month 2 
  1. 105,622.25 * 7.5 = 792,166.8750
  2. 792,166.88 / 1200 = 660.139066
  3. 660.14 + 105,622.25 = 106,282.39 
  4. 106,282.39 - 745.40 = 105,536.99 
$105,536.99 
Year 2 / Month 3 
  1. 105,536.99 * 7.5 = 791,527.4250
  2. 791,527.43 / 1200 = 659.60619
  3. 659.61 + 105,536.99 = 106,196.60 
  4. 106,196.60 - 745.40 = 105,451.20 
$105,451.20 
Year 2 / Month 4 
  1. 105,451.20 * 7.5 = 790,884.000
  2. 790,884.00 / 1200 = 659.07000
  3. 659.07 + 105,451.20 = 106,110.27 
  4. 106,110.27 - 745.40 = 105,364.87 
$105,364.87 
Year 2 / Month 5 
  1. 105,364.87 * 7.5 = 790,236.5250
  2. 790,236.53 / 1200 = 658.53041
  3. 658.53 + 105,364.87 = 106,023.40 
  4. 106,023.40 - 745.40 = 105,278.00
$105,278.00 
Year 2 / Month 6 
  1. 105,278.00 * 7.5 = 789,585.0000
  2. 789,585.00 / 1200 = 657.987500
  3. 657.99 + 105,278.00 = 105,935.99 
  4. 105,935.99 - 745.40 = 105,190.59 
$105,190.59 
Year 2 / Month 7 
  1. 105,190.59 * 7.5 = 788,929.4250
  2. 788,929.43 / 1200 = 657.441191
  3. 657.44 + 105,190.59 = 105,848.03 
  4. 105,848.03 - 745.40 = 105,102.63 
$105,102.63 
Year 2 / Month 8 
  1. 105,102.63 * 7.5 = 788,269.72500
  2. 788,269.73 / 1200 = 656.891441
  3. 656.89 + 105,102.63 = 105,759.52 
  4. 105,759.52 - 745.40 = 105,014.12 
$105,014.12 
Year 2 / Month 9 
  1. 105,014.12 * 7.5 = 787,605.9000
  2. 787,605.00 / 1200 = 656.338250
  3. 656.34 + 105,014.12 = 105,670.46 
  4. 105,670.46 - 745.40 = 104,925.06 
$104,925.06 
Year 2 / Month 10 
  1. 104,925.06 * 7.5 = 786,937.95000
  2. 786,936.95 / 1200 = 655.781625
  3. 655.78 + 104,925.06 = 105,580.84 
  4. 105,580.84 - 745.40 = 104,835.44 
$104,835.44 
Year 2 / Month 11 
  1. 104,835.44 * 7.5 = 786,265.80000
  2. 786,265.80 / 1200 = 655.221500
  3. 655.22 + 104,835.44 = 105,490.66 
  4. 105,490.66 - 745.40 = 104,745.26 
$104,745.26 
Year 2 / Month 12 
  1. 104,745.26 * 7.5 = 785,589.45000
  2. 785,588.45 / 1200 = 654.657875
  3. 654.66 + 104,745.26 = 105,399.92 
  4. 105,399.92 - 745.40 = 104,654.52
$104,654.52 

 

Total of the Year 2 results  $1,261,720.93 
Divided by 12
This is the Annual Average Outstanding Balance
$105,143.410833333333 
Multiplied by the Annual MIP Rate (.005)  $525.7170541667 
Rounded to two (2) decimal places  $525.72 
Divided by 1 + Upfront MIP Factor (1 + .0225)  $514.1515892421 
Rounded to two (2) decimal places $514.15 
Divided by 12  $42.8458333333 
Rounded to two (2) decimal places
This is the Monthly MIP
$42.85 
Multiply Monthly MIP by 12 

This is the Annual MIP

$514.20

Pseudocode

Input Values

interest  = Interest Rate

mip       = Annual MIP Rate

months    = Years Since Amortization Date * 12

orig_mtg  = Original Mortgage Amount

p_i       = Monthly Principal & Interest

upfront   = Upfront MIP Factor

hold_val  = A variable to store intermittent results

total_amt = A variable to sum the last 12 months

BEGIN

   last_val = orig_mtg

   total_amt = last_val

   FOR (I = 2 TO months)

        hold_val = last_val * interest

        [ROUND hold_val to 2 places after the decimal]

        hold_val = hold_val / 1200

        [ROUND hold_val to 2 places after the decimal]

        hold_val = hold_val + last_val

        hold_val = hold_val - p_i

        last_val = hold_val

        total_amt = total_amt + last_val

        IF (REMAINDER(I / 12) = 0) AND (I <> months) THEN

           total_amt = 0

        END IF

   NEXT I

   total_amt = total_amt / 12

   total_amt = total_amt * mip

   [ROUND total_amt to 2 places after the decimal]

   total_amt = total_amt / (1 + upfront)

   [ROUND total_amt to 2 places after the decimal]

   total_amt = total_amt / 12

   [ROUND total_amt to 2 places after the decimal]

   PRINT:  Monthly Premium = total_amt

END