So I have a dilemma here when it comes to optimizing student loan prepayment. Here’s the scenario.
Let’s say I currently owe 140K in student loans and I’m on a 7-year repayment plan. The loans consist of the following
30K at 7.75%
60K at 6.5%
30K at 8.25%
20K at 6.05%
Let’s say that I now have 35K which I can use to pre-pay the principal of the loans. How should I allocate the 35K-prepayment among the four loans to maximize my benefits? That is, I want to minimize the total interest over the life of the 4 loans.
My first intuition is to divide the 35K among the four loans in proportion to their remaining principals, but that seems inefficient because it makes sense to pay off the higher-interest loans first. However, it also seems inefficient to pay off the higher-interest loans like the 8.25% one entirely first, since in 7-year amortized payment plans most of the interest are paid in the first few years.
I don’t think there’s anything cleverer than “pay off the highest interest balance first”. So retire the 8.25% and put the rest towards the 7.75%.
The amortization schedule doesn’t really matter, because if you pay down the principal early, you don’t pay the interest at all. It’s not like you’ll hand them 30k and they’ll say, “good, you’ve paid of the interest in advance, now let’s work on the principal”.
The most efficient way to do it if you will continue to afford monthly payments of the same amount as it would’ve been if you had not prepaid is to pay off the 8.25% loan entirely, put the rest of the money (5k) toward the 7.75% loan, and then pay toward the 7.75% loan in addition to the regular monthly payment, each month prepay the amount you would’ve been paying on the 8.25% loan too. Once the 7.75% loan is paid off, prepay the amounts of both paid-off loans to the 6.5% loan.
If you calculate it out, you’ll find that this approach will give you the least total interest paid.
That would be my intuition as well. However, I have been playing with a mortgage calculator and paying off the higher-interest loans entirely does not seem to be optimal.
You are wrong. Post exactly what numbers you are entering into the calculator and what results you get and we should be able to point out what is wrong.
You probably aren’t considering that the monthly payment is higher if you don’t pay off the highest interest loan first. The only modifier should be if some loans are private and some are stafford - make sure you can’t consolidate to a lower rate before you determine which loans are really “highest interest”.
Here are the amortization tables for 2 loans. We assume that we have 100K to pre-pay the principle.
100K principal, 6.5% interest.
100K principal, 8.25% interest.
Scenario A: pay off the second loan (8.25%) with the 100K and pay the first loan (6.5%) monthly for 7 years. (Essentially, we just have one 100K 6.5% loan)
From the first table, the total payments are 125,645.27, so interests are 25,645.
Scenario B: split 100K into payments of 50K for each of the two loans. Each loan will have 50K remaining on their principals.
From the first table, locate the month and year at which the remaining principal is 50K. This occurs 46 months into the loan (Feb, 2017), so we have 38 months left at 1484/month payment. Total interest paid over remaining 38 months are 148438 - 50000 = $6392
From the second table, the 50K point occurs at 47 months into the loan (Mar, 2017), so we have 37 months left at 1571/month. Total interest paid is 157137 - 50000 = 8127.
So total interest under this scenario is 8127 + 6392 = 14,519.
My understanding is that student loans, unlike secured loans like mortgages, can not be refinanced to a lower rate. From Student Loan Consolidation - Finaid,
“The interest rate on a [consolidated student loan] is the weighted average of the interest rates on the loans being consolidated, rounded up to the nearest 1/8 of a percent and capped at 8.25%.”
Could the larger balance at 6.5% be whats confusing? Its a lower rate, but a much larger loan with not insignificant interest.
Granted I agree that the best course would still be to eliminate the highest interest debt first, but I could see where volume vs flow rate could make for some confusion.
Hm… I was all ready to jump in and say that you should pay off the highest rate first in its entirety, but I’m getting similar results to you in my amortization tables. Total interest if you split the principal payments across the two loans is ~$12k rather than ~$25k if you just retire the 8.25% loan.
A quick test seems to indicate that for the two-loan case the optimal strategy is somewhere around $55k to the 8.25% loan and $45k to the 6.5% loan. Eyeballing it that seems to be how you get the interest portion of the next payment to be equal (about $296 in your test case), but that might just be a coincidence.
The reason you are getting those numbers is because you are paying off the 50-50 split faster (38 months) instead of paying 7 years (60 months) in the 100-0 case. Borrowing a dollar for seven years will accrue more interest than borrowing it for 3.
To make a fair comparison you need to calculate interest if you paid the same amount for the 100-0 loan. In other words, in case 100-0 you are paying LESS each month than the 50-50 case (but for longer). If you paid 1484+1571 per month in the 100-0 case, you should pay off the loan faster and with less interest (i.e., the loan would be paid off in less than 38 months and therefore cost less overall).
The other benefit of paying off a loan entirely, is you remove a mandatory monthly payment. This gives you the option to pay more (see suggestion above by Deegeea) but can simply pay the minimum if things get tight.
It’s not wrong; it’s just failing to take a very significant factor into account. If you do not pay off both loans fully, then you continue to make full payments on both, and you shorten the lifetime of both loans. If you pay off one fully, then you end up making smaller monthly payment, but over a much longer period of time. The difference in timespan is more significant here than the difference in interest rate.
If instead you pay off the higher interest loan, and in addition make larger payments on the remaining loan equal to what you were paying for both loans, then you will end up with a lower total amount of interest.
What he is confusing is the payment amount under each scenario. In scenario A, he is assuming a monthly payment of about $1,484 per month (the payment on the 6.25% loan ). In scenario B, he is assuming a payment of $1,484 plus a payment of $1,571 for the 8.25% loan. Paying $3,055 towards a loan is going to pay it off much faster than paying $1,484, hence less interest. If the OP can pay off the highest interest rate loans off first, but still manage the total payments, that would be the best.
The simplest answer is minimizing the total interest paid is not the proper criterion. You want to minimize the present value of the total payments made where you calculate all the present values at your opportunity cost. This means pay off the highest rate loan first.
Ah, that makes more sense. I wasn’t considering that when you split the early payment you end up paying much more per month going forward. Obvious in retrospect.
So the punchline is continue to pay the most you can afford, and any principal payments over the minimum should go toward the note(s) with the highest rate.