# 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?

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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

In such a situation, the interest earned on the funds would be more than the interest charged on the extra principal you would have paid off, thus at the end of that period of time you would have more funds overall.

Instead of thinking of the \$500k loan as a single loan at 3%, think of it as 500 separate “mini” loans each at 3%.

You have \$1,000. You can either pay off 1 of the mini loans at 3% or earn 5%. That’s it. That’s your choices.

The other 499 mini loans (or \$499k total balance) will be there whether you put the \$1,000 towards the loan or the interest opportunity.

3% of \$500k is indeed a lot of money, but so is 3% of \$499k.

When it comes to deciding if you’re going to put the \$1000 towards paying down that debt what matters is how much interest you prevent by paying it down. In this case you go from 3% of \$500k (\$15,000) to 3% of \$499k (\$14,970). This move only shaves off \$30 in interest per year.

By contrast, if you can put that \$1000 into an account that earns 5% interest then that’s \$50 per year.

In addition to the interest bearing account just being more money it also will give you more flexibility–if you have a sudden need for \$1000 then it’s a lot less painful to pull the \$1000 out of an account than it is to put it on a credit card with super high interest rate.

If you put \$1000 toward a 500k loan, then you have a 499k loan. So yes, while the amount of interest on a 500k loan is a lot, the amount of the loan only changes by \$1000 (500k to 499k). So what matters is what changes, so the comparison should be \$1,000 in a 5% interest bank account or \$1,000 less on a 3% interest loan.

Percentages are percentages, the \$ amount doesn’t matter.

If putting money towards Investment A earns you 5% after tax and paying extra on Loan B saves you 3%, then your money is better off in Investment A, minus any personal feelings on holding debt.

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Example time:

Let’s take a \$200k loan @ 7% over 30yrs, if you put \$105/mo extra you would save ~\$65630 over 24yrs.

If you took \$105/mo earning say 9% after-tax, that would be ~\$70440 in interest over 24yrs.

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?

Regardless of the total balance, all you’re concerned about is the impact on that \$1000. You can save it and earn \$50 or you can pay down your loan and save \$30. Each year, it’s the same affect. That \$1000 can earn you another \$50 or the lower balance on your loan saves you another \$30.

ok lets math it out:

500k 3% intersst 30 years = 258k in interest and 759k total repayment

1k extra payment same terms = 140k in interest 640.4k total repayment & 18 year payoff

1k/mo into savings earning 5% for 30 years = **480k interest gained**