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:
- Details for first loan for 100.000 over 10 years.
- Details for second loan for 80.000 over 15 years are split in two parts first 10 years and the last 5 years (10 to 15) because it seems that it is not possible to change the monthly payments nor to add additional payments.
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.