Loan Interest Payment Puzzle / Question

[bennyboy]

Instead of thinking of the individual debt values or trying to calculate the total interest in different scenarios, you should think more of the value of the payment money for a clear answer to the question.

If I gave you two savings accounts paying 5% and 3%, where would you put your money? Obviously, the 5%.

Now, if you think of your payment as compounding negative debt (read: savings), things should look clear: NO MATTER WHAT, given limited funds, you will most benefit by putting your money wherever it is most magnified by the interest rate. Pay off the 5% debt first-- and it doesn't matter whether it's for $1 or $1 million.

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My financial planner has always advised me to always pay down higher interest rate debt first.   That may not be strictly mathematically correct, however.

Also - as I can pretty reliably get significantly better than 5% ROI, I wouldn't exactly be in a big hurry to pay either off, compared to investing.

Good point.  I have some government-underwritten low-interest loans (like 1%).  Those will be paid off as soon as I see pigs flying in front of the bank, because if I can't make at least 10% a year on my money, I don't deserve to have ANY.

[GUBU]

Good point.  I have some government-underwritten low-interest loans (like 1%).  Those will be paid off as soon as I see pigs flying in front of the bank, because if I can't make at least 10% a year on my money, I don't deserve to have ANY.

So you think you can make five times what the economy does, continuously? I hope you never get into bed with a proper wheeler dealer.

[bennyboy]

Good point.  I have some government-underwritten low-interest loans (like 1%).  Those will be paid off as soon as I see pigs flying in front of the bank, because if I can't make at least 10% a year on my money, I don't deserve to have ANY.

So you think you can make five times what the economy does, continuously? I hope you never get into bed with a proper wheeler dealer.

Yes, but not by investing in Mutual funds or anything, but rather by using the money to expand my business.  I'm up against this decision all the time-- given enough money to pay off a debt, do I do it?  Or do I use that money in hand to hire new staff, rent new property, and so on?

The issue is this: your personal expenses don't scale with business growth, but your profits do, so you want to scale as much as you can handle without overtaxing yourself and losing reputation by providing bad service or losing your control of your brand or whatever. When you're just turning the corner, a 10% growth in custom can mean doubling or tripling your net profits.

The debt game is a race condition, because added income requires more investment, but it ALSO means you have the capability of paying off debts even faster than before: you are hoping that your increased income will amount to more than the increased cost of the debt in monthly installments-- and also that the bubble doesn't burst, leaving you with 15% loans that used to be 4%, and fucking your profit margin forever.

This is different than the OP, where someone has presumably car or mortgage payments to make, and an income that doesn't scale with the debt. I've been in that condition too, and it means buying big bags of rice and oatmeal, driving nothing but used cars for a few years, and taking nothing more than day-trips until all those loans are paid off.

. . . starting with the highest-interest loan, no matter what.

[pocaracas]

This was a puzzle / question I encountered earlier today and I found it quite interesting.

Suppose that you have a $2,000 loan which accrues 5% interest each month, and a separate $20,000 loan that accrues 3% interest each month. At the end of each month (after interest has been accrued) you have $2,000 in savings that you can use on one of the loans. Assume that interest accumulates before you make your payment. Also assume that if you have less than $2000 left on one of the loans, you can use the amount left after interest and paying it off on the other loan.

The question is: which loans should you pay off first in order to reduce the total amount of interest you accrue.

If we can use those $2,000 in monthly savings any way we want, maybe there's a better way than using it all in one or the other loan... maybe a 3/5 to the higher interest loan and 2/5 to the lower interest one?...

Google sheets for quick and dirty spreadshiting:
https://docs.google.com/spreadsheets/d/1...sp=sharing


I tried to start both loans at the same level of 20k...
Interestingly, I was wrong... It's always better to pay off the higher interest loan, while the other just accumulates interest... provided you don't get prosecuted for not paying that other low interest loan.

(yeah yeah yeah, the spreadshit isn't perfect... sue me! I did it in 10 or 15 minutes and tried out a few combos)

A follow-up question (which I don't have the answer to) is: what is the optimal strategy for paying off the debt to reduce the total amount of interest accrued, assuming that you can split your $2,000 between the loans each month (i.e. put $100 on one, and $1900 on the other).

oh look.... that's what my alpha value does... I knew I hadn't invented it!
An alpha of 1, makes you spend everything on loan1 first; an alpha of 0 makes you spend everything on loan2 first...
My spreadshit doesn't work so well when you pay off loan2 before loan1.... there's no check for it... and I think I might enter the realm of circular referencing if I try... so... meh.

Anyway, you pay the least amount of interest for alpha=1, so paying everything on the highest interest loan.

[bennyboy]

Interestingly, I was wrong... It's always better to pay off the higher interest loan, while the other just accumulates interest... provided you don't get prosecuted for not paying that other low interest loan.

That's because ALL effects under the umbrella of that interest rate are magnified-- debts, payments, savings, withdrawals, whatever. It's strange that debt payment is so confusing, because with all other ways of dealing with money, things seem very clear.

Savings: If you had a 3% and 5% savings account, you'd ignore the 3% totally and put money in the 5%.
Withdrawal: You'd definitely withdraw money from the 3% savings account first, because the 5% one benefits you more.
Debts: Given the choice, you'd choose a 3% loan over a 5% one.
Payments: this thread and a lot of ??? But no, it really is this simple: your payment's value ALSO compounds at 5%. So your $1000 payment eventually has a value of $1050, and so on. I guess people don't consider this because it's kind of a "negative space"-- we can't intuitively understand "compounded interest that is lacking from the debt."


Maybe THIS idea should put this all to rest: if you could borrow MORE money at 3%, should you? Of course-- you'd use it to pay off the 5%!