Mortgage finance principal with two loans - find optimum & average rate

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Compare a single mortgage with two mortgages, find optimum, average interes

The conditions are that

  • interest rate is fixed for the term,
  • monthly payments can be changed 2 times between 1%/12 up to 10%/12 of the principal (interest + 150 up to 1500 monthly)
  • additional payments are allowed once per year up to 5% of the principal.

One way is to finance the full principal (p= 180000) using a single loan. To make it easier to compare the alternatives the fixed monthly payment c is set to 1000.

The results below are from a german online calculator:

Opt  term   p        i      c      rem. debt  paid-i    Sum paid to p
A    10y    180000   1.29   1000   76.620     16.620    103.380
B    13y    180000   1.56   1000   47.449     23.449    156.000
C    15y    180000   1.79   1000²  16.461     27.752    161.291
D1    10y   100000   1.29    800   11.291      7.291     96.000
D2    15y    80000   1.79    200³  12.695     16.696     84.000

Option D1+D2: The 200³ means that at the end of D1 (term = 10 years), the 800 payment from D1 would be used to add additional payments to D2 up to 9600/year. The 9600 can be divided by

  • 4000 (5% additional payment once per year)
  • 5600 (monthly payment 10%/12 = 666 since i already pay 200 the remaining amount is 12*466,66 ~ 5600).

The remaining debt of D1 (11.291) would be paid at the end of D1 without refinancing it.

Option C: has an additional payment of 11.291 made at May 2027. This is to make it easier to compare it to Options D1 + D2.

Initial Questions

It seems that Option D1,2 are my best bet;

        paid interest   paid to principal  rem. debt after 15y
C       27.752          161.291            16.461
D1+D2   23.987          180.000*           12.695

I would like to know:

  • what the average interest is if D1 (10 years) and D2 (15 years) are combined
  • if there is a better option for D1 and D2 under the condition that the remaining debt after a term should be below 13.000.
  • if it would be better to pay more to D2 at the beginning
  • if a diffential can be formulated to find the optimum

Update to adress comment

I used the other calculator:

and got these results

Yr  Debt        payments    interest    Repay       rem Debt

1   100.000,00  9.628,69    1.233,20    8.395,49    91.604,51
2   91.604,51   9.628,69    1.124,90    8.503,79    83.100,71
3   83.100,71   9.628,69    1.015,20    8.613,49    74.487,22
4   74.487,22   9.628,69      904,09    8.724,61    65.762,61
5   65.762,61   9.628,69      791,54    8.837,15    56.925,46
6   56.925,46   9.628,69      677,54    8.951,15    47.974,31
7   47.974,31   9.628,69      562,07    9.066,62    38.907,68
8   38.907,68   9.628,69      445,11    9.183,58    29.724,10
9   29.724,10   9.628,69      326,64    9.302,05    20.422,05
10  20.422,05   9.628,69      206,65    9.422,05    11.000,00

Sums           96.286,94    7.286,94   89.000,00    11.000,00

For the second loan i created two calclulations; the result for the first 10 years for the second loan of 80.000

Yr   Debt        payments    interest    Repay       rem Debt

1    80.000,00   2.400,00    1.412,37      987,63   79.012,37
2    79.012,37   2.400,00    1.394,69    1.005,31   78.007,07
3    78.007,07   2.400,00    1.376,70    1.023,30   76.983,77
4    76.983,77   2.400,00    1.358,38    1.041,62   75.942,15
5    75.942,15   2.400,00    1.339,74    1.060,26   74.881,89
6    74.881,89   2.400,00    1.320,76    1.079,24   73.802,65
7    73.802,65   2.400,00    1.301,44    1.098,56   72.704,09
8    72.704,09   2.400,00    1.281,78    1.118,22   71.585,86
9    71.585,86   2.400,00    1.261,76    1.138,24   70.447,62
10   70.447,62   2.400,00    1.241,39    1.158,61   69.289,01

Sums 80.000,00  24.000,00   13.289,01   10.710,99   69.289,01

And the result for the second part (10-15 years) for the remaining debt from the second loan.

Yr   Debt       payments    interest     Repay       rem Debt

1   69.289,01   7.999,20    1.174,86    6.824,34    62.464,67
2   62.464,67   7.999,20    1.052,70    6.946,50    55.518,17
3   55.518,17   7.999,20      928,36    7.070,84    48.447,33
4   48.447,33   7.999,20      801,79    7.197,41    41.249,92
5   41.249,92   7.999,20      672,96    7.326,24    33.923,67

Sum 69.289,01   39.996,00   4.630,66    35.365,34   33.923,67

Since the condition for the loan are that the sum of monthly payments can only be up to 10% of the loan i had to adjust the monthly payments to 666,60 (80000 * 10% /12). The additional payment once per year up to 5% (4000) are not included.

Question

The questions reamin the same (see above initial questions). Is there a formula to calculate the best loan split and payment plan to minimize the cost for borrowing the money.