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Why Loan Payments Are Lower When Made at the Start of the Month

Article Quant Q&A · Author: Computernerd
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Summary

The document compares monthly loan installments paid at the beginning versus the end of each month. Its example uses a fixed principal, annual interest rate, and repayment term, and reports a lower installment for the beginning-of-month schedule. The explanation is that an earlier payment reduces the outstanding balance before interest accrues over the coming month.

This is a timing effect: with payments at the start of a period, each installment is applied sooner, so less interest accumulates on the remaining balance. The discussion is brief and offers no derivation of the payment formula or broader comparison of loan conventions. It also contains an apparent spreadsheet-function inconsistency: the same final argument is shown for both schedules, even though that argument typically distinguishes beginning- and end-of-period payments. The stated figures should therefore be treated as an illustration of payment timing, not as independently verified calculations.

Key ideas

  • Paying at the start of each month reduces principal earlier than paying at month-end.
  • A lower outstanding balance over the month means less interest accrues.
  • The document illustrates the timing effect with a fixed-rate, fixed-term loan example.
  • Its spreadsheet formulas appear identical for both schedules, so the reported amounts are not verified by the shown formulas.

Tags

Fixed incomeStatistics
Full text
# Why is it cheaper to repay monthly loan at the start of the month


# Why is it cheaper to repay monthly loan at the start of the month












Assuming I borrow $50000 from the bank where the details are as follow

```
Loan amount : 50000
Annual interest rate : 6%
Repayment mode : At then end of the month
Loan repayment period : 60 months
```

Using MS Excel whereby I utilise the PMT method : `=PMT(6%/12,60,50000,0,1)`

I have to make a monthly repayment of $966.64

However if repayment mode is at the start of the month utilising the PMT method : `=PMT(6%/12,60,50000,0,1)`

I have to make a lower monthly repayment of $961.83

Can any kind soul explain to me why it is cheaper to repay the loan at the start of the month??

## Answer by Stefan Voigt (score 2)

https://quant.stackexchange.com/a/22942

If you make your repayment at the beginning of the month you do not have to pay accrued interest of the amount for the month. So, paying already 961.83$ at the first of each month makes a subtle difference to paying the same amount at the end of the month as you have to pay interest on this open position during those 30 days.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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