Loan Interest Payment Puzzle / Question

[brewer]

My loss of interest is compounding.

[Pat Mustard]

P.S. Both loans are at hefty rates. the 5% per month compounds up to 75%c. (1.05^12) and the 3% one to slightly under 50%.

[Tiberius]

Tazzy I don't think your calculations are correct, but I'm not sure where it's gone wrong.

Steel's first result matches mine but I think he has a bug when he calculated the second result (paying off the larger loan first) because somehow the interest for that loan ends up being higher than the first result which makes no sense.

My results:

---

If you pay off the $2k loan first, you pay $5166 in total interest payments.

If you pay off the $20k loan first, you pay $6002 in total interest payments.

So paying the smaller high interest loan first is better.

---

[SteelCurtain]

Oops, disregard that last one, had a bug in my code... (That was my birthday present to Tibs)

[SteelCurtain]

I think Tazzy's problem is in adding up the payments. Seems when he pays a partial payment he is calculating it as a full payment plus the partial payment both times.

[Pat Mustard]

I'll look them over tomorrow when I'm with working brain.

[Pat Mustard]

I'll reply to meself as I can see where I went wrong last night:

Ok I did a quick excel working of the problem.

First paying the small loan first:
Small

Code:

Principle Interest Lump   payment balance
2000      1.05     2100   2000         100
100        1.05      105   2000       -1895

Big

Code:

Principle Interest Lump     payment balance
20,000.00 1.03    20,600.00 0.00       20,600.00
20,600.00 1.03    21,218.00 1,895.00   19,323.00
19,323.00 1.03    19,902.69 2000       17,902.69
17,902.69 1.03    18,439.77 2000       16,439.77
16,439.77 1.03    16,932.96 2000       14,932.96
14,932.96 1.03    15,380.95 2000       13,380.95
13,380.95 1.03    13,782.38 2000       11,782.38
11,782.38 1.03    12,135.85 2000       10,135.85
10,135.85 1.03    10,439.93 2000        8,439.93
8,439.93 1.03     8,693.13 2000        6,693.13
6,693.13 1.03     6,893.92 2000        4,893.92
4,893.92 1.03     5,040.74 2000        3,040.74
3,040.74 1.03     3,131.96 2000        1,131.96
1,131.96 1.03    1,165.92 2000         -834.08

Ok so Small before big gives you 16 monthly payments of $2,000 plus a final one of $1,165.92 totalling $33,165.92 total payment.

Let's do it the other way shall we.
Big

Code:

Principle Interest Lump        payment balance
20,000.00 1.03     20,600.00 2,000.00 18,600.00
18,600.00 1.03     19,158.00 2,000.00 17,158.00
17,158.00 1.03     17,672.74 2,000.00 15,672.74
15,672.74 1.03     16,142.92 2,000.00 14,142.92
14,142.92 1.03     14,567.21 2,000.00 12,567.21
12,567.21 1.03     12,944.23 2,000.00 10,944.23
10,944.23 1.03     11,272.55 2,000.00 9,272.55
9,272.55 1.03      9,550.73 2,000.00 7,550.73
7,550.73 1.03      7,777.25 2,000.00 5,777.25
5,777.25 1.03      5,950.57 2,000.00 3,950.57
3,950.57 1.03      4,069.09 2,000.00 2,069.09
2,069.09 1.03      2,131.16 2,000.00 131.16
131.16 1.03         135.09 2,000.00 -1,864.91

Small

Code:

Principle Interest Lump payment balance
2,000.00 1.05 2,100.00 0.00 2,100.00
2,100.00 1.05 2,205.00 0.00 2,205.00
2,205.00 1.05 2,315.25 0.00 2,315.25
2,315.25 1.05 2,431.01 0.00 2,431.01
2,431.01 1.05 2,552.56 0.00 2,552.56
2,552.56 1.05 2,680.19 0.00 2,680.19
2,680.19 1.05 2,814.20 0.00 2,814.20
2,814.20 1.05 2,954.91 0.00 2,954.91
2,954.91 1.05 3,102.66 0.00 3,102.66
3,102.66 1.05 3,257.79 0.00 3,257.79
3,257.79 1.05 3,420.68 0.00 3,420.68
3,420.68 1.05 3,591.71 0.00 3,591.71
3,591.71 1.05 3,771.30 0.00 3,771.30
[b]1)[/b] 3,771.30 1.05 3,959.86 2,000.00 1,959.86
1,959.86 1.05 2,057.86 2,000.00 57.86
57.86 1.05 60.75 2,000.00 -1,939.25

Second one comes out at 16 payments of $2,000 and a final payment of $60.75 giving $32,060.75.

My workings say that you will be better off by $1,000 or there abouts if you pay off the bigger loan first of all before paying the smaller one. Despite the fact the smaller one accures more interest the differential between the interests isn't enough to ovetake the principle differentials in the timeframe of full payment.

I'll run a half and half scenario in a minute, just want to post this first.

Problem 1) Every line after the inserted bold 1 is wrong, because as our glorious Imperator says I made a double payment of $1,000 that month. Should read

Code:

3,771.30     1.05     3,959.86     135.09     3,824.77
3,824.77     1.05     4,016.01     2,000.00     2,016.01
2,016.01     1.05     2,116.81     2,000.00     116.81
116.81     1.05     122.65     2,000.00     -1,877.35

Which means 17 payments of $2,000 and a final payment of $122.65, which is $34,122.65, meaning my original statement was wrong, it is better to clear the small loan first.

The first set of calculations are right as far as I can see.
Oh dear, and the half and half calcuations has another error, a copy pasta one. The last two lines of the big loan payments show $2,001 and $2,002 payments, because I forgot to ensure I was copying the cells rather than filling a series. This means an underpayment of $5.03 due to my original calculations.

The formulae in the spreadsheet are correct, both cases were down to errors in my inputting of figures.

[Jackalope]

Excellent, it looks like I won't need to fire my financial advisor after all.

[Jackalope]

It's pretty clear what the answer is mathematically, but I think you can noodle it out another way.

Each month, I have X dollars I can apply to competing debts above and beyond what the minimum payments are. Here's the thing - by making that principal payment today, you are only avoiding future interest on the amount of the principal payment.

The total amount of the loan is irrelevant for the purpose of applying this one principal payment - you're paying interest on that money regardless. You avoid more future interest on the amount of this payment by applying it to the loan with the higher interest rate.

Repeat this exercise each month and I see no reason why the analysis should change.,

[mlmooney89]

I'm just sitting here like dude... I work as a loan assistant at a bank... pay off the smaller one cause I said so.

Y'all bring out the math and proof. lol