# Is this a weekly compounding loan amortization schedule?

I am currently having a disagreement with my colleagues regarding whether a loan is compounding or not.

I have linked below an image of a amortization schedule for a 52 week term for a \$50,000 loan. The loan has a weekly interest rate of 0.5%, which is applied each week on the previous week's closing balance.

My colleagues believe that the below loan is NOT a compounding loan. I believe the loan IS compounding, and that it's compounding weekly.

My colleagues believe it's not a compound loan because they believe interest is paid down to zero each week, and the closing balance only moves by the principal amount. For example, looking at the first week, they say the \$1,094.34 pays the \$250.00 of interest to zero at the end of the week (with the residual going to pay down principal by \$844.34), and that therefore no interest carries over to the following week (and if no interest carries over, then it's not a compounding loan).

My arguement is that the principal balance was decreased by the repayment amount, and then subsequently increased by the interest amount, and that therefore the interest balance is reflected in the closing principal (and therefore this interest carries over to the following week where it is compounded).

I strongly believe I am correct here, but am having difficulty in articulating or arguing why. Am I going crazy, and if not, how do I construct an argument to prove that it's a weekly compounding loan?

Edit: Follow up question, if the below loan is NOT compounding, then does that mean I can’t calculate the Effective Interest Rate for the loan =(1+0.5%)^(365/7)? My understanding is that EIR includes compounded interest.

Amortization schedule:

If you pay the full amount of interest each period, then it makes no difference if the loan is "compounding" or not - there's nothing to "compound", and you pay the same amount either way.

When it matters is if you don't pay down the interest completely (or at all). If the loan compounds, then the next period's interest will be calculated based on the principal outstanding and the amount of accrued interest. Some loans will call this "capitalized" interest, meaning the interest amount is effectively added to the principal. If the interest is calculated on the principal only, then the loan is a "simple" interest loan.

Compounding is much more evident in investments and savings accounts where it's clear that the amount of "interest" (or earnings) is included when calculating the earnings for the next period. With loans it's not so obvious, but growth rates are often calculated based on equivalent compounding rates, so the investment can be compared to a similar-risk investment that does compound (like a savings account).

And your calculation for EIR is still accurate - what that means is "if this loan accrued interest annually instead of weekly, and I made no payments, what would the interest rate be that would give me the same amount of interest.

Interest cannot compound here - the payments are indeed applied to the interest first and the remainder to the principal.

Your point of view that

the principal balance was decreased by the repayment amount, and then subsequently increased by the interest amount, and that therefore the interest balance is reflected in the closing principal (and therefore this interest carries over to the following week where it is compounded).

provides a different picture to the same situation, which would also lead to the same numbers. And if we wouldn't separate interest from the principal, it would be this way (more or less). But for several reasons, interest is kept separate from the principal and shown separately.