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Calculating Periodic Weighted Interest Rates on Amortizing Debt

Article Quant Q&A · Author: hannes101
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Summary

The document considers how to calculate an interest rate for a fixed-rate loan portfolio over periods shorter than a year. Its example uses a loan repaid in equal monthly installments, with each payment divided into interest and principal repayment. The question is whether monthly interest should be measured against the debt outstanding during that period rather than treating the annual rate as the monthly rate.

The accepted response says to align the interest amount with the debt balance over the relevant accrual period, noting that the stated balance for a period may need correction because interest accrues on the balance before that payment. For later periods, it describes aggregating remaining interest and relating it to the outstanding debt, then annualizing using the time interval shown. The example is limited to the stated amortizing loan and day-count convention; it does not provide a general portfolio weighting procedure or address differing loan terms, accrual rules, or payment timing.

Key ideas

  • A periodic interest measure should relate interest accrued to the debt balance that generated it.
  • For an amortizing loan, the balance before a payment may be the relevant exposure for that period.
  • The response annualizes remaining-period interest using the time basis in its example.
  • Portfolio calculations may require conventions beyond the single-loan example.

Tags

Fixed incomeStatistics
Full text
# Calculation of Weighted Interest Rate based on Outstanding Debt


# Calculation of Weighted Interest Rate based on Outstanding Debt












I would like to know what's the way on how to calculate the weighted average interest rate for a loan portfolio properly, especially when looking at periods shorter than a year. The basic definition is, that the Weighted Average Interest Rate = Interest Paid in Period / Total Debt.

I think the question becomes a bit clearer, when I use an example. Please assume a loan of 10000 and an annual interest rate of 5%, which should be paid back in 12 monthly installments. Based on this loan I would like to know the average weighted interest rate in each month. Based on the simplest calculation the annual weighted interest rate would be 5%. But I thought in case of a monthly perspective it is necessary to look at the monthly interest expense relative to the debt outstanding. That would mean the interest part of the repayment divided by the debt outstanding.

```
Period  Payment  Interest   Repayment   Debt Outstanding
   1    856.07        41.67   814.41    9185.59
   2    856.07        38.27   817.80    8367.79
   3    856.07        34.87   821.21    7546.58
   4    856.07        31.44   824.63    6721.95
   5    856.07        28.01   828.07    5893.88
   6    856.07        24.56   831.52    5062.37
   7    856.07        21.09   834.98    4227.39
   8    856.07        17.61   838.46    3388.93
   9    856.07        14.12   841.95    2546.97
  10    856.07        10.61   845.46    1701.51
  11    856.07        7.09    848.99    852.52
  12    856.07        3.55    852.52    0.00
```

That would for example mean that my weighted interest rate in Period 8 would be 17.61 divided by 3388.93, which would result in a monthly average interest rate of 0.0052.

Which is the correct way of calculating a weighted average interest rate, based on fixed-rate mortgages.

## Answer by MattR (score 0, accepted)

https://quant.stackexchange.com/a/31303

In first place you need to fix the outstanding debt, because in period 12, you are actually calculating interest over period 11 debt. In second place, you are right about using the interest part of the repayment divided by the debt outstanding. In the specific case of Period 8 and forward, assuming the other payments have already been payed, you only need to focus on the remaining payments. That said, your Weighted Average Interest Rate would be your monthly average interest rate annualized:

- Interest in Period 8 = ((17.61 + 14.12 + 10.61 + 7.09 + 3.55) / 4227.39)*360/150

- Interest in Period 9 = ((14.12 + 10.61 + 7.09 + 3.55) / 3388.93)*360/120

- Interest in Period 10 = ((10.61 + 7.09 + 3.55) / 2546.97)*360/90

- Interest in Period 11 = ((7.09 + 3.55) / 1701.51)*360/60

- Interest in Period 12 = (3.55) / 852.52)*360/30

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