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Calculate Mortgage Payment Including Taxes Insurance

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									Chapter 13




        Your Money
            and      13.4


         Your Math


                        1
Buying a House


                 13.4




                    2
Down Payment and FHA Loan Amount

Step 1. Calculate the minimum cash investment: 3% of price.
Step 2. Calculate the FHA down payment:
                                                      13.4
      Acquisition price – FHA loan amount

Down Payment: Higher value between steps 1 and 2
Loan amount: Acquisition price – down payment



                                                         3
1. The Browning family of Colorado (a low closing cost state)
   want to buy a $77,000 house.
a. If they can get a loan of 80% of the value of the house, what
   is the amount of the loan?
b. What will be the down payment on this loan?
c. If they use an FHA loan, what will be the minimum cash
   investment?
a. 80% of $77,000 = $61,600                              13.4
b. $77,000 – $61,600 = $15,400 (20% of $77,000)
c. Cash investment is 3% of $77,000 = $2310 (at least)
   FHA down payment = Acquisition Price – FHA loan

                    = $77,000 – (97.65% of $77,000)
                    = $ 77,000 – $75,190.50
                    = $1809
  Down Payment = $2310 (which is their minimum cash investment)
                                                                4
2. Find

a. The minimum cash investment.
b. The maximum FHA loan amount.

    Sale Price                    State
     $75,000                   Jackson, MS               13.4

a. Cash investment is 3% of $75,000 = $2250 (at least)
   FHA down payment = $75,000 – .9775 x $75,000
                    = $ 75,000.00 – $73,312.50
                    = $1687.50
   Down Payment = $2250 (minimum cash investment)
b. Loan Amount = $75,000 – $2,250 = $72,750
                                                            5
3.    Find the total monthly payment, including the taxes
      and insurance, for the given mortgage loan.
      (Use Table 13.5 on pp. 922-3)

                  Time              Annual      Annual
     Amount Rate (Years)            Taxes      Insurance
     $90,000     9%         25      $1200        $960
                                                              13.4

     Table 13.5 yields $8.39

     90 x $8.39 = $755.10

     Monthly Taxes and Insurance = (1200 + 960) / 12 = $180

     Monthly Payment = $755.10 + $180 = $935.10
                                                                 6
Formula to Find the Monthly Payment
              for a Loan
  The monthly payment M for a loan of P dollars
  for n months at monthly rate i is           13.4




               Pi                      r
                                       P m
  M 
      1  (1  i)  1  1  m  mt  
                  n
                     
                               r
                                          
                                         
                                                 7
4. Assume that the buyer in example 2 is paying closing
   costs of $700.

a. What is the acquisition cost?
b. What is the maximum FHA loan amount?
c. Use the formula to find the monthly payment if the
   loan is at 7½% for 25 years.
                                                              13.4
a. Acquisition price = $75,000 + $700 = $75,700
   Minimum cash investment = $75,700 - 0.9775x$75,000 = $2387.50
b. Loan amount = $75,700.00 – $2387.50 = $73,312.50
                 r 
               P
                 m
                                            
                                              075
                                  73312 .50 0.12

                             1    12
                                      0.075 1225  
c. M                                                   $541.77
                      mt 
              
         1  1  r 
                     
                                   1                   
                 m                                
                                                                 8
5. The Bixley family has a $50,000 mortgage loan at 10%
   for 30 years.

a. What is the family’s monthly mortgage payment?

b. How many payment will the family have to make in all?
                                                           13.4
c.   What is the total amount the family will pay for principal
     and interest?

d. What is the total interest the family will pay?



                                                              9
                50000  012
                         .10
a. M                                    $438.79
         1 
         
         
                 0.10 ( 1230 )
                1 12              
                                    
                                    
                                                         13.4
b. Number of payments = 12 30 = 360


c. Total Payments = 360 $438.79 = $157,964.40


d. Total Interest = $157,964.40  $50,000.00 = $107,964.40
                                                             10
                   Example
5. Suppose you purchase a home and obtain a
   20-year loan of $225,000 at an annual interest
   rate of 6.0%. Find the amount of interest that
   will be paid on the loan over the 20 years.
                    Solution                                   13.4

                    225000  .06 
          M                 12
                                                   $1611.97
               1  1     12 
                             .06 ( 12*20)
                                             
       Total Cost  $1611.97 12  20  $386,872.80

     Interest  $386,872.80  $225, 000  $161,872.80
                                                                  11
                             Example
6. Joseph has signed a $144,000 mortgage with
   monthly payments of $1,127.71. The loan is
   a 30-year fixed-rate mortgage at 8.7%.
   Determine the unpaid balance after 19 years.
                             Formula                                               13.4
         M 1  (1  i ) ( 12*( t  x ))         M 1  (1  12 ) ( 12*( t  x )) 
                                                                r

   B                                          
                         i                                         12 
                                                                     r


    B – unpaid balance       M – monthly payment             i – interest rate per period
    r – interest rate        t – term of mortgage            x – elapsed years

                             Solution
             $1127.711  (1         0.087 ( 12*(30 19)
                                           )                   $95, 603.14
        B
                                       12

                                0.087 
                                  12                                                     12
       Amortization Schedule
 The following is the usual headings for an amortization schedule.

             Payment               Interest      Portion       Principal at
                        Payment
             Number               per Period   to Principal   end of Period



Payment zero is the amount of the loan.
The periodic payment is found using the formula on slide 7.
Interest per Period is found using the formula I = Prt.
Portion to Principle is Payment  Interest per Period. Interest per Period
must always be paid first.                                                         13.4
Principal (Balance) at end of period is Previous Balance  Portion to Principal.
This balance is the amount needed to pay off the loan early.
The last payment is done differently then the rest of the payments.
  a. Principal at end of Period must be zero.
  b. Portion to principal is the previous balance.
  c. Interest per period is calculated as usual.
  d. The last payment is the sum of the Interest per period and Portion to Principal.
     This amount is usually different than all of the others because it most zero out
      the loan.
                                                                                      13
                    Example
Ethan has borrowed $3000 at 6% compounded quarterly and
has agreed to pay the loan in quarterly payments over a two
year period. Make an amortization schedule for the loan.

   Payment                Interest      Portion       Principal at
              Payment
   Number                per Period   to Principal   end of Period
      0                                                $3000.00

      1                                                              13.4
      2

      3

      4

      5

      6

      7

      8
                                                                        14
                       Solution
       M 
                        0.406   $400 .75
                      $3000
           1  1  0.06 ( 4*2) 
                                  
                      4           
   Notice the last payment has not been filled in yet.
Payment                   Interest      Portion       Principal at
            Payment
Number                   per Period   to Principal   end of Period
   0                                                   $3000.00
                                                                     13.4
   1         $400.75

   2         400.75

   3         400.75

   4         400.75

   5         400.75

   6         400.75

   7         400.75

   8                                                                    15
          Solution Continued
I1 = $3000.00(0.06)() = $45.00      I2 = $2644.25(0.06)() = $39.66
I3= $2283.16(0.06)() = $34.25       I4 = $1916.66(0.06)() = $28.75
I5= $1544.66(0.06)() = $23.17       I6 = $1167.88(0.06)() = $17.51
I7= $ 784.64(0.06)() = $11.77       I8 = $ 395.66(0.06)() = $ 5.93
Payment                  Interest       Portion       Principal at
            Payment
Number                  per Period    to Principal   end of Period
   0                                                   $3000.00
                                                                       13.4
   1        $400.75      $45.00        $355.75         2644.25
   2         400.75       39.66         361.09         2283.16

   3         400.75       34.25         366.50         1916.66

   4         400.75       28.75         372.00         1544.66
   5         400.75       23.17         377.58         1167.88
   6         400.75       17.51         383.24           784.64
   7         400.75       11.77         388.98          395.66

   8         401.59        5.93         395.66            0.00            16
                                                                          END

								
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