Trading/Investing Thread - Page 95

On January 17 2022 08:59 micronesia wrote:
My math doesn't take into account inflation, time value of money, or strategies to make extra payments beyond the first month

On January 17 2022 09:22 Blitzkrieg0 wrote:


If you ignore every reason the correct answer is correct then it becomes wrong doesn't seem like a valuable use of your time.

On January 17 2022 10:26 LegalLord wrote:

I mean, disregarding time value of money is essentially saying the same thing as disregarding the answer. TVM is the basis by which you calculate the relative value of each payment. Fundamentally, money you borrow has a cost (in the form of an interest rate), you set one of payment or duration, and the other of payment/duration is the result. At any point in time, retiring an obligation with the highest cost is the optimal strategy.

Perhaps the most useful way to look at the problem is to see where you land after 10 years. You start at time 0 (today) and have taken out the loans A and B. You plan to make minimum payments to pay off A in 30 years and B in 10 years, with the exception of an extra $200 to be paid towards a principal right now.

At the end of the 10 year point, that $200 as applied to A would have reduced $296 in principal plus accumulated interest (10 years at 4%), and B would have reduced $358 in the same. Clear advantage to B, but at that point B has been repaid so it will no longer be accumulating more interest. However, your last payment into B would have been reduced by that $358, which you can choose to put into payments towards the A loan. That's money that your last B payment would not have been reduced by if you had not put that $200 in at the start, so it's not extra money being introduced into the loan repayment. And it's pretty clear that $358 will compound into a larger loan savings than $296 over the 20 years that follow.

Were you to choose to take that $358 payment reduction out of the system and not apply it towards A, that's taking money that would have otherwise been committed to loan payments that you choose to use for a different purpose instead. Yes, that might happen, but you might also choose to refinance A or something. Ultimately, that $200 would do more good in B for 10 years followed by A for 20 than in A for the whole 30 years. Which goes back to "the obvious answer is the correct one."

On January 17 2022 07:21 micronesia wrote:
I have a finance question I'm not 100% sure of the best way to answer related to paying off loans. I figure I'll share it with the brain trust.

I just took out two loans: a 30-year loan of 300k with 4% interest and a 10-year loan of 100k with 6% interest. For the first payment, I want to make an extra one-time $200 payment towards principle. If my ultimate goal is to save money, should I put that payment towards the 300k loan or the 100k loan?

I think conventional wisdom is to put the payment towards the higher-interest loan. However, if you put the extra payment towards the 30-year loan, you are saving a lot on compound interest. Which is the smarter thing to do, and more importantly, why?

I ask because I may be in this situation in the future, although I made up the numbers to keep it simple. The answer might change depending on the exact numbers chosen though.

edit: I think the answer is different than the answer to the question of which loan to attack first to get debt free in general

On January 17 2022 12:26 KwarK wrote:

Is this a serious question?

On January 17 2022 12:41 DarkPlasmaBall wrote:


Others have directly answered which loan they think technically saves you a bit more money, but I'll just throw in the suggestion that - while paying off the principal is always preferable - I don't really think it matters which loan you pick, given how negligible $200 is compared to $300,000 and $100,000. If you were going to pay off $20,000 up front, it would be a more worthwhile question, but $200 is a drop in the bucket for either one.

On January 17 2022 12:42 micronesia wrote:

No I didn't actually take out the loans. Yes, I was wondering if my math (discussed in a later post) was correct or not. No, my math being correct is clearly not "useful" for the reasons subsequently discussed. I was wondering why my math was contrary to conventional wisdom but then figured it out by reading some articles and figuring out what assumptions they were making that I was not.

On January 17 2022 13:32 Vivax wrote:
I'm curious about what other people somewhere said that suggests there's a mistake in the math.

Between the lines this reads as if you're escogitating ways to make money by taking on debt.

On January 17 2022 13:58 KwarK wrote:

Every additional dollar of principal paid down saves you the interest on that dollar for the period. So the question was whether it was better to save $12 or $8 each period. $12 is better because $12 > $8.

On January 17 2022 08:59 micronesia wrote:

When I thought about this I realized you don't derive any realized benefit until the final month of the loan (assuming you don't sell the house/etc early). An extra early payment will either reduce the size of the final payment (by an amount greater than the extra payment) or will allow the loan to end in an earlier month entirely. In my example, attacking the smaller but higher interest rate loan will derive a benefit in a much earlier year (more valuable) than attacking the larger loan with an extra up-front payment. The part where I'm struggling is to determine if time value necessarily overwhelms any other competing benefits. I'll show a bit of math further down.

This all made perfect sense to me but I chose to define the loan by duration rather than monthly payment amount. You could of course define it using either number and the other would be calculated for you up front.


Isn't there a competing effect where the larger loan's interest is going to compound for much longer, though (if we disregard time value of money for now)?


For comparison, here is my math:

If I pay off the 300k loan normally, I pay 215,607 in interest by the end. If I cut the principle by 200 at the beginning, I pay 215,465 in interest. By injecting 200 at the beginning, I saved 142 over the life of the loan.

If I pay off the 100k loan normally, I pay 33,224 in interest by the end. If I cut the principle by 200 at the beginning, I pay 33,158 in interest. By injecting 200 at the beginning, I saved 66 over the life of the loan.

This is the calculator I was using: https://www.bankrate.com/calculators/home-equity/additional-mortgage-payment-calculator.aspx (I kept "additional principle payment" 0 for this experiment).

My math doesn't take into account inflation, time value of money, or strategies to make extra payments beyond the first month. Is my math wrong somehow? It seems to show that, everything else being equal, you are better off pumping a bit of extra $$ into the 300k loan if your sole goal is to reduce total interest paid across all loans.