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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 FHA Single Family Housing Policy Handbook 4000.1 for the annual and upfront MIP rates currently in effect.

Monthly MIP Computation Steps Example
Step 1: Compute annual average outstanding balance based on the original amortization schedule (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.

\$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.

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.

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

*Based on the original amortization schedule.

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