How To Optimize Loan Payback?

Question

Say I have a $100k 3% mortgage with min $1k payment, $10k 5% car loan with $100 min payment and $1k 20% credit card with $50 min payment. If I have $1500 to spend, I need to split that to pay back at least the minimum on each loan. A rule of thumb is to overpay high interest first - but that means I pay more interest longer on the bigger loans. There must must be a formula that picks monthly splits to maximize net worth at the end of the payment sequence?

With that formula in hand, I should be able to include investments (flipping the sign on the balance) and optimize savings alongside loans.

Answer 1

A rule of thumb is to overpay high interest first - but that means I pay more interest longer on the bigger loans.

If you're dealing with fixed rates it's always most efficient to pay off the higher effective interest rate first, regardless of loan duration. Every extra dollar you pay toward either loan is a dollar you don't pay interest on again, so the only question is how much interest will that dollar of debt cost you.

The minimum payment is based on the loan duration, but otherwise loan duration has no impact on deciding what to pay of first.

A thought experiment that some have found helpful is to imagine that instead of having two loans that you have 110,000 loans of $1 each. 10,000 of those at 5% and rest at 3%. They are all one year loans that renew for another year if they go unpaid. Each 5% loan costs you $0.05 per year (simple interest), and each 3% loan costs you $0.03 per year. So every $1 you pay toward a 5% loan saves you $0.05, but that's a dollar you couldn't pay toward a 3% loan, which costs you $0.03, you still save $0.02 per year per dollar put toward 5% loan(s).

Effective interest rate is important because if there is a tax advantage to some debt it could create a preference between two otherwise comparable rates. Not likely an issue in your case unless you were already itemizing deductions for other reasons. I'm also assuming no prepayment penalties.

Answer 2

Hart is absolutely right about paying the highest rate first. Sometimes if the rates are close I'd suggest paying the lowest balance first (to get it knocked out), but your lowest balance happens to be your highest rate, so that's taken care of either way.

However, I wanted to address this:

With that formula in hand, I should be able to include investments (flipping the sign on the balance) and optimize savings alongside loans.

The problem with investing while paying off debt is that you're effectively borrowing money to invest. The interest you pay on the loans is fixed, but the return you get on your investments is variable, and can go negative (as it has this year). Plus there are psychological factors that make it so that you end up paying on debt much longer than you should.

I know several people who borrow to the hilt so that they can max out their investments (thinking they'll earn more than they spend in interest), and they are constantly stressed over the market. An alternative (which I have done) is to prioritize debt, get everything paid off except the mortgage, then focus on investing (and other savings). You'll have more money in your budget to invest and will have no trouble making up for lost time after the debt payments are gone.