User Guide: Appendix > Interest Year Calculations
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Interest Year Calculations

Interest Year determines the calculation method for the per diem interest of the loan and will thus affect the Annual Percentage Yield.

Interest Year in the Nortridge Loan System is defined by a Numerator and a Denominator, both of which can be one of five values: 360, 364, 365, 366, or ACT. Since the Interest Year is defined as a ratio of two instances from these five values, there are 25 possible interest year definitions:

 
N = 360
N = 364
N = 365
N = 366
N = ACT
D = 360

360 / 360
(Prin × Int) ÷ (# of annual payments x # of days in current payment period)

364 / 360
((Prin × Int) ÷ 360) × (364 ÷ ACT)

365 / 360
((Prin × Int) ÷ 360) × (365 ÷ ACT)

366 / 360
((Prin × Int) ÷ 360) × (366 ÷ ACT)

ACT / 360
((Prin × Int) ÷ 360) × (ACT ÷ ACT) = (Prin × Int) ÷ 360

D = 364

360 / 364
((Prin × Int) ÷ 364) × (360 ÷ ACT)

364 / 364
((Prin × Int) ÷ 364) × (364 ÷ ACT) = (Prin × Int) ÷ ACT

365 / 364
((Prin × Int) ÷ 364) × (365 ÷ ACT)

366 / 364
((Prin × Int) ÷ 364) × (366 ÷ ACT)

ACT / 364
((Prin × Int) ÷ 364) × (ACT ÷ ACT) = (Prin × Int) ÷ 364

D = 365

360 / 365
((Prin × Int) ÷ 365) × (360 ÷ ACT)

364 / 365
((Prin × Int) ÷ 365) × (364 ÷ ACT)

365 / 365
((Prin × Int) ÷ 365) × (365 ÷ ACT) = (Prin × Int) ÷ ACT

366 / 365
((Prin × Int) ÷ 365) × (366 ÷ ACT)

ACT / 365
((Prin × Int) ÷ 365) × (ACT ÷ ACT) = (Prin × Int) ÷ 365

D = 366

360 / 366
((Prin × Int) ÷ 366) × (360 ÷ ACT)

364 / 366
((Prin × Int) ÷ 366) × (364 ÷ ACT)

365 / 366
((Prin × Int) ÷ 366) × (365 ÷ ACT)

366 / 366
((Prin × Int) ÷ 366) × (366 ÷ ACT) = (Prin × Int) ÷ ACT

ACT / 366
((Prin × Int) ÷ 366) × (ACT ÷ ACT) = (Prin × Int) ÷ 366

D = ACT

360 / ACT
((Prin × Int) ÷ ACT) × (360 ÷ ACT)

364 / ACT
((Prin × Int) ÷ ACT) × (364 ÷ ACT)

365 / ACT
((Prin × Int) ÷ ACT) × (365 ÷ ACT)

366 / ACT
((Prin × Int) ÷ ACT) × (366 ÷ ACT)

ACT / ACT
((Prin × Int) ÷ ACT) × (ACT ÷ ACT) = (Prin × Int) ÷ ACT

The value: ACT represents the actual number of days in the current year. All Interest Years containing the value of ACT emulate other interest year calculations but may emulate different interest years depending on the leap year status of the current year.

Interest Year

In Non-Leap Year Emulates

In Leap Year Emulates

ACT / 360

365 / 360

366 / 360

ACT / 364

365 / 364

366 / 364

ACT / 365

365 / 365

366 / 365

ACT / 366

365 / 366

366 / 366

ACT / ACT

365 / 365

366 / 366

360 / ACT

360 / 365

360 / 366

364 / ACT

364 / 365

364 / 366

365 / ACT

365 / 365

365 / 366

366 / ACT

366 / 365

366 / 366

To calculate the per diem, first multiply the interest rate (r) by the principal (p) to derive the annual interest (i).

To calculate the per diem (daily) interest, use the following equation where:

i = annual interest
z = per diem interest
n = numerator of interest year
d = denominator of interest year
l = number of days in current year (365 if a non-leap year and 366 if a leap year)

The same equation, written in single line format (as a computer equation) would look like this:

The Interest Year 360/360 is a special case. In this case, the per diem interest is the annual interest divided by the number of payments in a year, divided by the number of days in the current payment period. This interest year is inherent in the amortizing equations, and while a Fixed AmortizationType of interest method where interest is accrued daily on the amount of principal specified in the amortization schedule. Early or late payments do not affect the accrual. Principal reduction transactions will cause the schedule to re-amortize. The interest is non-compounding and is typically calculated on a 360/360 interest year. loan could be done with other interest years, 360/360 is assumed for Fixed Amortization loans because this is the only interest year calculation where the accrual and an amortization schedule built from the amortizing equations will directly synchronize.

For each interest year, you may calculate the Annual Percentage Yield (APY) by multiplying the Annual Percentage Rate (APR) by the factor listed in the table below (not accounting for fees and charges).

Interest Year

APY factor (Non-Leap)

APY factor (Leap Year)

360 / 360

1

1

364 / 360

1.01111

1.01111

365 / 360

1.01389

1.01389

366 / 360

1.01667

1.01667

ACT / 360

1.01389

1.01667

360 / 364

0.98901

0.98901

364 / 364

1

1

365 / 364

1.00275

1.00275

366 / 364

1.00549

1.00549

ACT / 364

1.00275

1.00549

360 / 365

0.98630

0.98630

364 / 365

0.99726

0.99726

365 / 365

1

1

366 / 365

1.00274

1.00274

ACT / 365

1

1.00274

360 / 366

0.98361

0.98361

364 / 366

0.99454

0.99454

365 / 366

0.99727

0.99727

366 / 366

1

1

ACT / 366

0.99727

1

360 / ACT

0.98630

0.98361

364 / ACT

0.99726

0.99454

365 / ACT

1

0.99727

366 / ACT

1.00274

1

ACT / ACT

1

1

Example:

A 10% APR loan with an Interest Year of ACT/360 (the Interest Year with the highest possible yield) will have an APY of 10.1389% in non-leap years and 10.1667% in leap years.

Over the life of a 30 year loan with a starting principal of $100,000, this would result in an additional $2,183 in accrued interest.



Updated: 2018.08.30


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