Calculating Loan Balances with Actual Day-Count Accruals

Summary

The document asks how to calculate the remaining principal on a loan when interest accrues using Actual/360 or Actual/Actual day-count conventions. It contrasts these methods with a 30/360 amortization, for which a level-payment annuity formula can express the balance as the future value of the original principal less the future value of payments.

With actual day counts, accrual periods can vary in length, so payments and the balance path may not match the assumptions behind a level-payment annuity formula. The question wonders whether the day-count differences can be represented as a correction to the standard formula or whether an amortization schedule is needed. No answer or worked method is included, so the document does not establish a closed-form formula or demonstrate an adjustment.

Its useful framing is that balance calculations depend on the accrual convention and payment schedule. To calculate a specific balance reliably, the relevant dates, cash flows, and accrual rules must be specified; the document leaves the solution open.

Key ideas

• A 30/360 level-payment loan can be represented using a future-value annuity calculation.
• Actual day-count conventions can produce accrual periods of different lengths.
• The question does not provide a formula or worked solution for Actual/360 or Actual/Actual balances.
• A reliable balance calculation depends on the loan’s dates, payment schedule, and accrual convention.

Tags

# Remaining Balance Formula for Actual/360 and Actual/Actual Accrual Methods


# Remaining Balance Formula for Actual/360 and Actual/Actual Accrual Methods












Is there a concise formula for calculating the remaining balance of a loan with actual/360 and actual/actual accruals?

I know for 30/360 amortizations, the remaining balance is just the FV of the principle less the FV of the loan payment annuity.

```
// Remaining balance for a loan amount of "princ" 
// and a monthly payment of "coupon" using a 30/360 accrual

Remaining Balance = princ * (1+r)^n - coupon * [((1+r)^n - 1) / r]
```

I know with actuals, we can't easily use the annuity formula, since we don't have level payments.

I was hoping there was a formula that can take into account these "errors", where the annuity assumes 30 day, missing the day in 31, compound the error at the same rate, allowing us to still calculate the accurate remaining balance.

Or do we have to build a full amortization schedule to compute?

For a refresher on accrual methods, here is a terrific blog post explaining the differences

Thank you!

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.