Which loan is more profitable to pay off first – an expensive one or a large one?

If you have two loans with different interest rates and for different amounts, and there is an opportunity to invest a certain amount in partial early repayment, which one should be repaid first?

It seems that intuition tells you that the expensive loan should be paid off first. But maybe it all depends on the loan amount and the amount of the early payment?

Let's check. After all, this is a very practical task.

I will consider a real example from my life – I have two mortgages.

First loan 600,000 rubles at 12%. Expensive and small.
Second loan 9,500,000 rubles at 11%. Volume and cheap.
Where is it more profitable to invest an early one-time payment of 100,000 rubles?

I decided to test the theory with mathematics Google Sheet “Two Credits”.

Classic train of thought

If you don't make an early payment at all, you will be paid 799,526 + 22,819,225 = 23 618 870.

If you invest 100,000 in a small expensive loan, you will pay 730,526 + 22,819,225 = 23 549 752.

If you invest 100,000 in a large cheap loan, you will pay 799,644 + 22,116,762 = 22 916 406.

It turns out that it is more profitable to pay off a larger loan early – on the invested funds 100,000 it turns out to be a benefit 633 345?

Work on mistakes

But despite the simplicity of the approach, it contains an errorwhich is not noticeable at first glance, but distorts the result.

Doubts should be generated already at the stage of definition, and under what conditions is one scenario more profitable than another, at what interest rates and loan amount ratios? It seems that the complexity of the question is a sign of its erroneousness.

The thing is that when we make an early payment on a more expensive loan, smaller in amount, its payments end earlier. As a result, the monthly cash flow decreases, and accordingly, the amount of payments is larger. That is, in two scenarios we violate the condition that the amounts of funds invested monthly must be the same, deliberately underestimating the amount of total payments in the case of early repayment of a small expensive loan.

That is, in everyday language, we were glad that we repaid a small loan early and decided not to invest the saved amount, violating the identity of the conditions for investing money in repaying the loan. Of course, if you reduce the contribution of money to repay the loan, the loan will cost more.

If you make an early payment of 100,000 rubles, an expensive small loan is repaid already in the 48th month. In this case, the Difference column shows the monthly difference in payments:

To maintain the same cash flow, you need to continue making payments on the first loan as scheduled, while, as expected, you pay off the more expensive loan early. ALWAYS more profitable, regardless of the size of the second loan.

And this is evident in the numbers – the difference for 100,000 is 34,358:

The amount of payments on a large cheap loan, taking into account the difference to maintain an equivalent monthly flow of 22,151,522:

The correct total amount of payments in this case is: 730,526 + 22,151,522 = 22 882 048.

This is less than the payment amounts. 22 916 406 with an early deposit into a large cheap loan.

In finance, you need to be very attentive to details; using only a credit calculator, it’s easy to make a mistake.

CONCLUSION: a more expensive loan must ALWAYS be repaid first, regardless of the loan amount