# 360 365 Interest

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So, how much interest do you pay per day? You would think the daily rate is 5%/365, but the legalese says that they are going to use a 360 day year, and so you pay 5%/360 per day for 365 days. In other words, assuming no payments to clutter up the math, the annual rate of interest (APR as the legalese calls it) is ((1 + .05/360)^365 – 1)x100%

For both 30/360 and actual/360, the daily interest rate is the annualRate/360. For 30/360, each month is considered to be 30 days. Thus, the monthly interest rate for on-time payments is annualRate*30/360, which is the same as annualRate/12. The regular monthly payment can be computed by: roundup(pmt(annualRate/12, termInMonths, -loanAmount), 2)

Per Diem Interest The difference between a 360-day and a 365-day year is relevant to the calculation of prepaid or per diem interest. This is interest for the period between the loan closing date and the first day of the following month. That calculation uses a daily interest rate.

interest rate greater than the nominal interest rate. Using the "365/360 US Rule Methodology" interest is earned for 365 days even though the daily rate was calculated using 360 days. Using the "monthly payment methodology" interest is earned on 12 thirty day months or in effect 360 days.

Day count convention for calculating interest accrued on U.S. Treasury bills and other money market instruments. Uses actual number of days in a month and 360 days in a year for calculating.

I was approached by a client asking me why does your bank use 360 days instead of 365 days when calculating the interest payment of a loan. I told him it’s some sort of a convention, but he wasn’t fully convinced. I looked up Wikipedia, but it doesn’t provide much detail. Why 360 Days Instead of

1. Convert the APR to a daily rate — Interest isn’t charged once per day, so APR is converted to a daily periodic rate, or DPR, by dividing the APR by either 360 or 365. For a 17% APR divided by 365,

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divide the APR by 365. So if your APR is 4 percent, the daily periodic interest rate is a little under 0.011 percent. Some banks and other credit issuers actually divide the APR by 360 rather than 365.