Why is it always more beneficial to earn a higher interest rate on a smaller amount of money vs paying more towards a significantly higher amount of money with a lower interest rate?

Question

I wasn’t sure if this was more of a personalfinance question or an explainlikeimfive question–

This is something I’ve always struggled with in terms of understanding in a simple way. Why is better to put $1000/mo in a account that gets you 5% interest rate, vs putting an extra $1000/mo towards a loan (for $500k) that has a 3% interest rate?

I know the former is the better approach, but I can never get it to “make sense” in my head as far as why we wouldn’t want to reduce the much higher balance first (since 3% of 500k is still MUCH higher than what you would earn on an investment that’s only growing by $1000/mo, despite the higher interest rate)

In: Economics

Answer 1

You kind of just have to do the math but the non math idea is that over the course of the loan, the higher interest rate comes out on top, but not necessarily month to month.

You are right that 3% of 500k is much bigger than 5% of a 1000. But that’s not really what you are comparing. For example, over the course of 50 months, both the principal of the loan and the savings amount to 500k (assuming 1000 per month of principal or saving like in your example) , but the interest rate is different. So if the principal amount is the same, then you are gaining the 2% different by choosing to invest that money at 5% rather than pay it off early at 3? Does that make sense?