Office of Planning, Environment, & Realty (HEP)

Planning • Environment • **Real Estate**

Attached are technical guidance, calculator instructions, and computer printouts. for your information and use in understanding, teaching and computing mortgage interest differential payments (MIDP) in accordance withthe Uniform Act and the government wide single rule published as 49 CFR Part.24, dated March 2, 1989.

The calculator programs are known to work with the Hewlett

Packard 12C, the Texas Instruments BAII, and the Radio Shack EC-

100. The programs may also work with other similar calculators.

Please be aware that there will be subtle differences in the answers as a result of the different programs.

A share ware computer disk is also available. It is written in the BASIC language and will work on any PC compatible computer. it is userfriendly, contains good explanatory material, provides printouts with explanations for the estimated and final MIDPs, and includes mortgage amortization tables. The disk can be used for training and copies can be made. It is not to be used for the ongoing computations of MIDPs. An agency personalized copy for that purpose can be ordered from the program developer for a fee of $150 as indicated in the literature. The program developer, Mr. Walter L. Sharpe, spent an extensive amount of time and effort developing the program and intends to provide future refinements to anyone purchasing the disk.

If you are interested in just the calculation of the MIDP, we also have a disc.made. available by the Michigan Department of Transportation. The disk requires LO TUS We will provide a copy of this program to anyone furnishing a formatted disk. Sample printouts of each program are enclosed.

Please share this information with all State, local, and other agencies, or consultants that may be performing displacing activities for your agency.

If you have any questions, please call Barbara J. Satorius (.202), 3662043, of the Federal Highway Administration, Office of RightofWay, Program Requirements Division, Policy Development. Branch.

**Mortgage Interest Differential Payments**

Information needed for computations:

Balance of Existing Mortgage | ______ | ^{1} Amount of new mortgage |
______ |

Interest rate of " " | ______ | Interest rate of new mortgage | ______ |

^{2} Monthly payment of " " |
______ | Points on new mortgage | ______ |

^{3} Term of new mortgage |
______ |

The initial computations for a mortgage interest differential payment for comparison purposes will be based on the data for the existing mortgage(s) available at the time the replacement housing payment is computed and one of the prevailing fixed interest rates (including points) for conventional mortgages in the area. If there is a range of interest rates and points available in an area that could be considered prevailing or typical, the Agency may use a prevailing fixed interest rate that will require the smallest mortgage interest differential payment by the Agency to maintain the same monthly payment for the same term for the new mortgage as existed on the old mortgage for the initial computation and offer. An example follows:

Balance of Old Mortgage | $50,000 |

Interest rate of Old Mortgage | 7% |

Monthly Payment of Old Mortgage | $458.22 |

Computed Remaining Term of Old Mortgage | 174 months |

Specific instructions for computing mortgage interest payments using the Hewlett Packard (HP 12C), the Texas Instruments (BAII), and the Radio Shack (EC100) calculators are located at the end of this section.

Available interest rates for fixed mortgages, for 15 years. (Use the rates for terms of mortgages that are at least as long as the remaining term of the old mortgage, i.e. the 15 year rates for terms of 15 years or less and the 30 year table for loans with remaining terms exceeding 15 years.)

Interest rates available for 15 year mortgage . | 9.5% with 3 points |

10% with 2 points | |

10.5% with 1 point | |

11% with 0 points |

The computed mortgage interest differential payments are as follows:

Amount to be financed | ||||

$43,201.92 | 9.5% w 3 pts | - 6797.24(buydown) | + 1296.08(points) | = $8093.32 |

$42,010.18 | 10.0% w 2 pts | - 7989.82 | + 840.20 | = $8830.03 |

$40,866.89 | 10.5% w 1 pts | - 9133.1 | + 408.67 | = $9541.78 |

$39,770.48 | 11% w 0 pts | - 10,229.52 | + 0 | = $10229.52 |

As demonstrated by this example, the prevailing interest rate that will provide maintenance of. monthly .payments of $458.22 at the least cost to the Agency is 9. 5$ .interest with : points.

The Agency may advise the displaced person that he/she may receive $8,093.32 for the mortgage interest differential payment, based.on the current mortgage rate of 9.5% interest plus 3 points, if a new mortgage is obtained in at least the calculated replacement mortgage amount of $43,201.92 and for at least 174 months.

Alternate Computations for smaller and/or Shorter Term New Mortgage

**A. New mortgage is smaller than calculated replacement mortgage amount.**

In the event the displaced person elects to obtain a mortgage smaller than the calculatedreplacement mortgage, the payment must be prorated. For example:

Old mortgage | New mortgage | |
---|---|---|

Balance | $50,000 | $40,000 |

Remain. term | 174 months | 174 months |

Int. rate | 7% | 5% |

points | 3 |

The previous buydown computation indicated. that a calculated replacement mortgage of $43,201.92 was necessary to obtain the estimated MIDP of $8093.32. To determine the MIDP in this example, divide the actual new mortgage amount, $40,000 by the calculated replacement mortgage amount, $43,201.92. The resulting factor, .92588, is multiplied by the estimated MIDP, $8,093.32, to give the reduced amount of $7,493.48 as the MIDP on the smaller new mortgage.

$40,000/$43,201.92 = .92588 .x 8093.32 = $7493.48 MIDP

(including points)

**B. Shorter term new mortgage**

In the event that the displaced person elects to obtain a mortgage for a shorter term than the remaining term of the old mortgage, it is necessary to compute a hypothetical monthly payment for the old mortgage at the old interest rate but at the shorter term of the new mortgage. This computed hypothetical monthly payment will be larger than the actual payment on the old mortgage. Take the previously used old mortgage example:

Old mortgage | New mortgage | |
---|---|---|

Remaining balance | $50,000 | |

Interest rate | 7% | 9.5% |

Monthly payment | $458.22 | |

Remaining term | 174 months | 120 months |

points | 3 |

Step 1: Compute a hypothetical monthly payment for old mortgage based on a 120 month payoff $580.54

Step 2: Compute a .calculated replacement mortgage using the hypothetical monthly payment of $580.54 per month, 120 months at 9.5% interest rate. The calculated replacement mortgage amount is $44864.83. The buy-down amount is the old mortgage balance of $50,000 less the calculated replacement mortgage of $44,864.83, = $5,135.17 + points of $1,345.95. (3% of $44,864.83), or a total of $6,481.11.

The displaced person would need to obtain a mortgage of at least $44,864.83 to receive a payment of $6,481.11.

**C. Smaller new mortgage and shorter term.**

A different computation is made if the new mortgage is both smaller and for a shorter term. Using the old mortgage figures cited above, with a new mortgage for $40,000, term of 120 months and 9.5% interestrate, the calculated replacement mortgage as computed in example B. ($44,864.83) is divided into the smaller new mortgage ($40,000) giving a factor of .89157 x the estimated MIDP of $6,481.11 (from example B) for a MIDP of $5,778.34.

The example computations in no way restrict the displaced person to any combination of mortgage amounts and/or terms for the new mortgage. The agency's sole restriction is that the MIDP payment will be computed on mortgage terms at the typical rates prevailing in the area, unless there is reason for a valid exception. The displaced person may obtain a fixed, rate mortgage, a variable interest rate mortgage, a mortgage with a balloon payment, or any other legitimate mortgage. For example, he or she could elect to get a $60,000 mortgage for 15 years at 11% and no points. He or she would be entitled to a mortgage interest differential payment of $10,229.52 (based on a new mortgage of at least the amount of old mortgage minus the calculated replacement mortgage, for a term not less than the remaining term on the old mortgage) . Even though the mortgage for 9.5% with 3 points is available, the mortgage for 11% is also a prevailing rate mortgage.

The displaced person should be fully informed of his or her options for new mortgages as well as the rudimentary skills necessary for, negotiating for replacement housing.

The agent may elect to provide to the displaced person the estimated MIDP amount for a new mortgage of the same term and amounts as for the old mortgage(s) only. The computations for mortgages of shorter terms and lesser amounts would not be provided. Instead, a statement would be provided as follows:

You are eligible for a mortgage interest differential payment of $_______. This payment is based on the remaining term and amount of the mortgage on your old dwelling and the current prevailing mortgage interest rate of interest with points.

This eligibility is premised on your obtaining a mortgage on your new property for a term of not less than months, the remaining term on your old mortgage, for not less than $_______.

If you elect to obtain a mortgage in a smaller amount or for a shorter term, a recomputation will be required and your payment will probably be smaller. Please contact your relocation agent for the necessary computations prior to commitment to such a loan.

The computation for the actual amount of the mortgage interest differential payment should be made as soonas all the new facts. are known. The necessary facts are:

Old mortgage(s) | New mortgage | ||
---|---|---|---|

Remaining Principal Balance | ________________ | Amount of new mortgage | ________________ |

Interest rate | ________________ | Interest rate - new mortgage | ________________ |

Monthly payment | ________________ | Points | ________________ |

Term | ________________ |

If the term of the new mortgage is at least as long as the .remaining term of the old mortgage, compute calculated replacement mortgage, and deduct this amount from the old mortgage to get the buy-down amount, to which you add the appropriate points, the sum of these two figures equals the MIDP.

**Multiple mortgages**

If there is more than one mortgage, compute the buydown by completing the computations for each mortgage. using the terms of that mortgage. If there is an old second..mortgage that has a higher interest rate than any available rate, the buydown amount will be 0, but you then add points to arrive at a MIDP; the points are still eligible even though the new mortgage is at a rate that does not exceed the old mortgage.

**Variable rate mortgage**

If the mortgage is a variable interest rate mortgage, use the mortgage balance, interest rate, and monthly payment amount that was in effect in the date of acquisition.

**Home equity loans**

If there is a home equity loan,.. use the lesser of the mortgage balance on the date of acquisition or 180 days prior to the date of initiation of negotiations. Use the interest rate and monthly payment in effect for the lowest mortgage balance.

**Mortgages with balloon payments**

If the mortgage has a balloon payment, use the mortgage balance, interest rate and monthly payment amount that was, in effect on the date of acquisition. The monthly payment is normally predicated on a term longer than the actual term of the mortgage, so the computed remaining term will be greater than the actual remaining term of the mortgage. Use of the computed remaining term will provide you with the appropriate MIDP.

**Buydown Mortgage Interest Differential Terminology**

Acquired dwelling | the dwelling being acquired for a project by the agency. |

Old mortgage | the remaining principal balance of the existing mortgage on the acquired dwelling. This is not necessarily the "'pay-of" figure since that can include penalties and escrow credits. |

Old interest rate | the interest rate in effect on the old mortgage at the time of closing on the acquired dwelling. |

Old monthly payment |
the monthly payment, principal and interest, that is actually required by the mortgage agreement on the acquired dwelling. |

Remaining term | the number of payments necessary to pay off the old mortgage given the old monthly payment and old interest rate. This is to be calculated by the agent computing the mortgage interest differential. |

New mortgage | the amount of the mortgage entered into on the replacement dwelling. |

New interest rate | the interest rate being charged on the new. mortgage at the time of closing on the replacement dwelling. |

New term | the term of the new mortgage. |

Points | the prepaid interest or discount points needed to secure the interest rate on the new mortgage. |

Prevailing interest rate and points | an interest rate and point combination commonly available in the area. This may be a range of rates and points. In special circumstances, the prevailing rate may be dictated by what the displaced person is actually able to secure. |

Calculated replacement mortgage | the amount which the agency calculates can be financed at the lesser of the new interest rate or prevailing rate which will maintain either the old mothly payment for the old term or the hypothetical monthly payment at the new term when the new term is shorter than the remaining term. |

Buydown amount | the difference between the old mortgage and the calculated replacement mortgage. |

Hypothetical monthly payment | the payment necessary to pay off the old mortgage at the old interest rate for the new term when the new term is shorter than the remaining term. |

MIDP | the buydown amount plus the points. |

Estimated MIDP | the amount the MIDP would be if the relocatee secures a new mortgage for at least as much as the calculated replacement mortgage. |

Turn calculator on ** ( on ) **

Clear financial memory **( f ) ( fin )**

**1. COMPUTING THE REMAINING TERM OF THE OLD MORTGAGE**

Explanation | Key entry | Screen shows |
---|---|---|

Enter remaining balance | ( 50000 ) ( PV ) |
50000 |

Enter interest rate & convert to monthly | ( 7 ) ( g ) ( 12% ) |
0.58 |

Enter monthly payment | ( 458.22 ) ( CHS ) ( PMT ) |
-458.22 |

Compute remaining term | ( n ) |
174 |

**2. CALCULATING THE MIDP**

Explanation | Key entry | Screen shows |
---|---|---|

Enter interest rate (new mortg.) & convert to monthly | ( 9.5 ) ( g ) ( 12% ) |
0.79 |

Enter remaining payments | ( 174 ) ( n ) |
174 |

Enter monthly payment | ( 458.22 ) ( CHS ) ( PMT ) |
-458.22 |

Compute replacement mortgage | ( PV ) |
43203.11 |

Compute points | ( .03 ) ( X ) |
1296.09 |

Compute MIDP as follows: | ||

Old mortgage - new mortgage (50,000 43203.11) = | 6796.89 | |

add points | 1296.09 | |

MIDP = | $8092.98 |

**3. ALTERNATE CALCULATIONS FOR SMALLER AND/OR SHORTER TERM REPLACEMENT MORTGAGES**

A. REPLACEMENT MORTGAGE IS SMALLER THAN CALCULATED REPLACEMENT MORTGAGE AMOUNT

Explanation | Key entry | Screen shows |
---|---|---|

Compute MIDP per 1 & 2 above | ||

Enter new (smaller) mortgage | ( 40000 ) ( enter ) |
40000 |

Enter calculated replacement mortgage amount & divide | ( 43203.11 ) ( ÷ ) |
0.92586 |

Multiply the factor (.92586) X the calculated MIDP (2-above) | ( 8082.98 ) ( X ) |
7483.70 |

$7483.70 is the MIDP for the smaller replacement mortgage. |

B. SHORTER TERM REPLACEMENT MORTGAGE

Explanation | Key entry | Screen shows |
---|---|---|

Enter remaining balance | ||

Enter new (smaller) mortgage | ( 50000 ) ( PV ) |
50000 |

Enter interest rate for old mortgage & convert to monthly | ( 7 ) ( g ) ( 12% ) |
0.58 |

Enter term of new mortgage & convert to months | ( 10 ) ( g ) ( 12X ) |
120 |

Compute hypothetical payment | ( PMT ) |
580.54 |

Go back to 2 and calculate MIDP using the hypothetical payment, new mortgage term & interest rate. (in our. example, $580.54, 120 months and 9.5%, respectively) | ||

Enter new interest rate, convert to monthly | ( 9.5 ) ( g ) ( 12% ) |
0.79 |

hypothetical payment | ( 580.54 ) ( PMT ) |
580.54 |

new term | ( 10 ) ( g ) ( 12X ) |
120 |

compute buydown | ( PV ) |
44865.02 |

compute points | ( .03 ) ( X ) |
1345.95 |

MIDP computation: | ||

old mortgage - buydown (50000 .44865.02) = | 5134.98 | |

add points | 1345.95 | |

Total MIDP = | $6480.93 |

C . SMALLER REPLACEMENT MORTGAGE & SHORTER TERM

Compute MIDP based on full calculated replacement mortgage for shorter term (example 3 B.)

Divide actual (smaller) replacement mortgage by buydown computed per 3 B.

Explanation | Key entry | Screen shows |
---|---|---|

Smaller mortgage | ( 40000 ) ( enter ) |
40000 |

buydown mortgage | ( 44865.02 ) ( ÷ ) |
0.89156 |

multiply factor x MIDP from 3B. | ( 6480.93 ) ( X ) |
5778.16 |

The MIDP based on the shorter term and smaller amount (a combination of examples 3A. & 3B.) is $5778.16, which includes the points.

*NOTE: You will find the totals on the HP 12C programs will be slightly different than the computed program or the TI program. This is because the 12C reports the last period as a full period, when it is actually a payment of less than a full payment. This could be corrected, but the difference is usually only a few cents and should not be of concern.

Turn calculator on ** ( on ) **

Put calculator in Financial Mode **( 2nd ) ( Mode ) **

**1. COMPUTING THE REMAINING TERM OF THE OLD MORTGAGE**

Explanation | Key entry | Screen shows |
---|---|---|

Enter remaining balance | ( 50000 ) ( PV ) |
50000 |

Enter interest rate | ( 7 ) |
7 |

Convert to monthly | ( ÷ ) ( 12 ) ( = ) |
0.5833333 |

store in %i | ( %i ) |
0.5833333 |

Enter monthly payment | ( 458.22 ) ( PMT ) |
458.22 |

Compute remaining term | ( 2nd ) ( n ) |
173.99705 |

**2. CALCULATING THE MIDP**

Explanation | Key entry | Screen shows |
---|---|---|

Enter interest rate (new) | ( 9. 5 ) |
9.5 |

Convert to monthly | ( ÷ ) ( 12 ) ( = ) |
0.7916667 |

store in %i | ( %i ) |
0.7916667 |

Enter remaining payments | ( 173.99705 ) ( n ) |
173.99705 |

Enter monthly payment | ( 458.22 ) ( PMT ) |
458.22 |

Compute replacement mortgage | ( 2nd ) ( PV ) |
43202.762 |

Compute points | ( X ) ( .03 ) ( = ) |
1296.0829 |

Compute MIDP as follows: | ||

Old mortgage new mortgage (50000 43202.762) = | 6797.2376 | |

add points | 1296.0829 | |

MIDP = | $8093.3205 | |

Rounded = | 8093.32 |

**3. ALTERNATE CALCULATIONS FOR SMALLER AND/OR SHORTER TERM REPLACEMENT MORTGAGES**

A. REPLACEMENT MORTGAGE IS SMALLER THAN CALCULATED REPLACEMENT MORTGAGE AMOUNT

Explanation | Key entry | Screen shows |
---|---|---|

Compute MIDP per 1&2 above | ||

Enter new (smaller) mortgage | ( 40000 ) ( ÷ ) |
40000 |

Enter calculated replacement mortgage amount & divide | ( 43202.762 ) ( = ) |
0.9258667 |

Multiply the factor (.9258667) x the calculated MIDP (2-above) | ( X ) ( 8093.3205 ) ( = ) |
7493.3362 |

$7493.34 is the MIDP for the smaller replacement mortgage. |

B. SHORTER TERM REPLACEMENT MORTGAGE

Explanation | Key entry | Screen shows |
---|---|---|

Enter remaining balance | ( 50000 ) ( PV ) |
50000 |

Enter old interest rate | ( 7 ) |
0.9258667 |

convert to monthly | ( ÷ ) ( 12 ) ( = ) |
0.5833333 |

store in %i | ( %i ) |
0.5833333 |

Enter term of new mortgage | ( 10 ) |
10 |

convert to months | ( X ) ( 12 ) ( = ) |
120 |

store in N | ( N ) |
120 |

Compute hypothetical payment | ( 2nd ) ( PMT ) |
580.54239 |

Go back to 2 and calculate MIDP using the hypothetical payment, new mortgage term & interest rate. (in our example, $580.54, 120 months and 9.5%, respectively) | ||

Enter new interest rate, convert to monthly | ( 9.5 ) ( ÷ ) ( 12 ) ( = ) |
0.7916667 |

store in %i | ( %i ) |
0.7916667 |

hypothetical payment | ( 580.54239 ) ( PMT ) |
580.54239 |

new term | ( 10 ) ( X ) ( 12 ) ( = ) ( N ) |
120 |

compute buydown | ( 2nd ) ( PV ) |
44865.018 |

compute points | ( X ) ( .03 ) ( = ) |
1345.9505 |

MIDP computation: | ||

Old mortgage buydown (50000 44865.018) = | 5134.982 | |

add points | 1345.9505 | |

Total MIDP = | $6480.9325 | |

rounded | 6480.93 |

C. SMALLER REPLACEMENT MORTGAGE & SHORTER TERM

Compute MIDP based on full calculated replacement mortgage for shorter term (example 3 B.)

Explanation | Key entry | Screen shows |
---|---|---|

Divide actual (smaller) replacement mortgage by buydown computed per 3 B. | ||

Smaller mortgage | ( 40000 ) ( ÷ ) |
40000 |

buydown mortgage | ( 44865.018 ) ( = ) |
0.8915632 |

multiply factor x MIDP from 3 B. | ( X ) ( 6480.9325 ) ( = ) |
5778.1611 |

Go back to 2 and calculate MIDP using the hypothetical payment, new mortgage term & interest rate. (in our example, $580.54, 120 months and 9.5%, respectively) | ||

Enter new interest rate, convert to monthly | ( 9.5 ) ( ÷ ) ( 12 ) ( = ) |
0.7916667 |

store in %i | ( %i ) |
0.7916667 |

hypothetical payment | ( 580.54239 ) ( PMT ) |
580.54239 |

new term | ( 10 ) ( X ) ( 12 ) ( = ) ( N ) |
120 |

compute buydown | ( 2nd ) ( PV ) |
44865.018 |

compute points | ( X ) ( .03 ) ( = ) |
1345.9505 |

The MIDP based on the shorter term and smaller amount (a combination of examples 3 A. & 3 B.) is $5778.16, which includes the points.

*NOTE: You will find the totals on the TI and the HP 12C will .be slightly different from each other and from the computer program. This is because the 12C reports the last period as a full period, when it usually is actually a payment of less than a full payment. This could be corrected, but the difference usually is only a few cents and should be of no concern.

We have used a floating decimal place and carried the figures out as far as the BA II screen shows. This was to avoid rounding errors but is not necessary if you prefer to fix the decimal place.

Turn BA II off **( OFF )**

URRPAC FHWA REL 3/92

^{1} The actual amount of the new mortgage is only of concern if it is less than the amount needed to befinancedtomaintainthe old mortgage.

^{2} If the term of the new mortgage 3s the same. as or greater than the term of the existing mortgage, use the monthly payment of the existing mortgage (s) to compute the number of months actually necessary to pay off the existing mortgage.

^{3} If the term of the new mortgage is less than the term of the existing mortgage(s), use the term of the new mortgage to compute the monthly payment necessary to pay off the existing mortgage using the shorter term.

Updated: 09/05/2014