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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??

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  • $\begingroup$ Hi computernerd, welcome to Quant.SE! muffin1974's answer really should be sufficient here. Smaller amount of money outstanding in time period => less interest. $\endgroup$
    – Bob Jansen
    Jan 27, 2016 at 12:34

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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.

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  • $\begingroup$ I dont understand the part "f you make your repayment at the beginning of the month you do not have to pay accrued interest of the amount for the month", could you elaborate on it $\endgroup$ Jan 27, 2016 at 8:14
  • $\begingroup$ @Computernerd This is a query about basic maths and understanding of how interest rates work. It is not really a question about quantitative finance. $\endgroup$
    – jwg
    Jan 27, 2016 at 8:20

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