# How is minimum payment calculated for this daily amortized loan?

I'm trying to figure out how the bank calculated the minimum payment for a personal loan.

• Starting Principle: \$6,800
• Interest Rate: 13.750%
• Loan Term: 36 months
• Payment Frequency: Monthly
• Start Date: Jan 5
• First Payment: Feb 2

I've been able to calculate the interest in a spreadsheet like this:

``````=ACCRINTM(Jan 5, Feb 2, 13.750%, 6800, 3)
``````

And this correctly comes out to \$71.726, which according to the bank is \$71.72. Assuming they rounded down here...?

They've calculated the minimum payment as \$231.47. I haven't been able to figure out how they got to this number.

The closest I've been able to get is with this:

``````=PMT(13.75%/12, 12*3, -6800, 0, 0)
``````

Which comes out to be \$231.583, \$0.113 off. I know that the above calculation is meant for monthly amortization.

I've tried this, which I got off a message board thread:

``````=roundup(pmt(fv(13.75%/360, 30, 0, -1)-1, 12*30, -6800), 2)*3
``````

But this comes out to be \$238.92, which is even farther off. I've tried adjusting the above to 365 and that gives me \$235.86. The other suggestions in that thread go well above \$231.

Does anyone know how I would calculate \$231.47?

• If the payment is monthly, why is the first payment not on February 5? – DJohnM Mar 29 '15 at 22:55
• @User58220 Start date is, or close to, when you start the loan. Daily amortized loans accumulate interest from the start date to the first payment date. The first payment date is typically about 1 month from the start date, but doesn't have to be the same day. Knowing both dates are important for calculating the exact interest. Might also be important for calculating minimum payment. Either way I'm still trying to figure out how the minimum payment is calculated. – Luke Mar 30 '15 at 23:50