payment (what I believe you call an "amortizing" loan) rather than the one with the fixed
payment. Using your example, if you pay $100,000 to reduce each $1,000,000 loan to $900,000, you'd save $13,227 interest on the first loan; but only $12,708 on the second loan.
, while the savings on the first loan are spread evenly over the 60 months, more savings on the second loan occur during the first 30 months than during the last 30. Because of this, the Internal Rate of Return (IRR) from paying an additional $100,000 is
(5%) for both loans. In fact the IRR is 5% for all six cases: the original $1,000,000 amount, the reduced $900,000 amount and the $100,000 reduction for both loans. [*] (The formulas use the Excel
Code: Select all
10 0 (1,000,000) (900,000) (100,000) (1,000,000) (900,000) (100,000)
11 1 18,871 16,984 1,887 20,833 18,750 2,083
12 2 18,871 16,984 1,887 20,764 18,688 2,076
13 3 18,871 16,984 1,887 20,694 18,625 2,069
14 4 18,871 16,984 1,887 20,625 18,563 2,063
15 5 18,871 16,984 1,887 20,556 18,500 2,056
16 6 18,871 16,984 1,887 20,486 18,438 2,049
17 7 18,871 16,984 1,887 20,417 18,375 2,042
18 8 18,871 16,984 1,887 20,347 18,313 2,035
19 9 18,871 16,984 1,887 20,278 18,250 2,028
20 10 18,871 16,984 1,887 20,208 18,188 2,021
21 11 18,871 16,984 1,887 20,139 18,125 2,014
22 12 18,871 16,984 1,887 20,069 18,063 2,007
23 13 18,871 16,984 1,887 20,000 18,000 2,000
24 14 18,871 16,984 1,887 19,931 17,938 1,993
25 15 18,871 16,984 1,887 19,861 17,875 1,986
26 16 18,871 16,984 1,887 19,792 17,813 1,979
27 17 18,871 16,984 1,887 19,722 17,750 1,972
28 18 18,871 16,984 1,887 19,653 17,688 1,965
29 19 18,871 16,984 1,887 19,583 17,625 1,958
30 20 18,871 16,984 1,887 19,514 17,563 1,951
31 21 18,871 16,984 1,887 19,444 17,500 1,944
32 22 18,871 16,984 1,887 19,375 17,438 1,938
33 23 18,871 16,984 1,887 19,306 17,375 1,931
34 24 18,871 16,984 1,887 19,236 17,313 1,924
35 25 18,871 16,984 1,887 19,167 17,250 1,917
36 26 18,871 16,984 1,887 19,097 17,188 1,910
37 27 18,871 16,984 1,887 19,028 17,125 1,903
38 28 18,871 16,984 1,887 18,958 17,063 1,896
39 29 18,871 16,984 1,887 18,889 17,000 1,889
40 30 18,871 16,984 1,887 18,819 16,938 1,882
41 31 18,871 16,984 1,887 18,750 16,875 1,875
42 32 18,871 16,984 1,887 18,681 16,813 1,868
43 33 18,871 16,984 1,887 18,611 16,750 1,861
44 34 18,871 16,984 1,887 18,542 16,688 1,854
45 35 18,871 16,984 1,887 18,472 16,625 1,847
46 36 18,871 16,984 1,887 18,403 16,563 1,840
47 37 18,871 16,984 1,887 18,333 16,500 1,833
48 38 18,871 16,984 1,887 18,264 16,438 1,826
49 39 18,871 16,984 1,887 18,194 16,375 1,819
50 40 18,871 16,984 1,887 18,125 16,313 1,813
51 41 18,871 16,984 1,887 18,056 16,250 1,806
52 42 18,871 16,984 1,887 17,986 16,188 1,799
53 43 18,871 16,984 1,887 17,917 16,125 1,792
54 44 18,871 16,984 1,887 17,847 16,063 1,785
55 45 18,871 16,984 1,887 17,778 16,000 1,778
56 46 18,871 16,984 1,887 17,708 15,938 1,771
57 47 18,871 16,984 1,887 17,639 15,875 1,764
58 48 18,871 16,984 1,887 17,569 15,813 1,757
59 49 18,871 16,984 1,887 17,500 15,750 1,750
60 50 18,871 16,984 1,887 17,431 15,688 1,743
61 51 18,871 16,984 1,887 17,361 15,625 1,736
62 52 18,871 16,984 1,887 17,292 15,563 1,729
63 53 18,871 16,984 1,887 17,222 15,500 1,722
64 54 18,871 16,984 1,887 17,153 15,438 1,715
65 55 18,871 16,984 1,887 17,083 15,375 1,708
66 56 18,871 16,984 1,887 17,014 15,313 1,701
67 57 18,871 16,984 1,887 16,944 15,250 1,694
68 58 18,871 16,984 1,887 16,875 15,188 1,688
69 59 18,871 16,984 1,887 16,806 15,125 1,681
70 60 18,871 16,984 1,887 16,736 15,063 1,674
--------- --------- ------- --------- --------- -------
Total 1,132,274 1,019,047 113,227 1,127,083 1,014,375 112,708
mo 1-30 566,137 509,523 56,614 594,792 535,313 59,479
mo 31-60 566,137 509,523 56,614 532,292 479,063 53,229
Interest 132,274 119,047 13,227 127,083 114,375 12,708
* You'd expect the IRR to be same for the original amount, the reduced amount, and the savings for both loans since all the figures in the "Reduced" column are 90% of those in the "Original" column and all those in the "Savings" column are 10%.