"Act/365" - Leap Years

Q

What is the impact of leap year on the "Act/365", or "Actual/365" Day Count Convention?

✍: FYIcenter.com

A

If look at the Accrued Interest on your term deposit in a leap year, you will see a higher amount than regular years.

Here is an example of a 5-year term deposit:

Principal:             $1,000.00 
Interest Method:       Simple Interest 
Interest Frequency:    12 (Monthly) 
Interest Rate:         5.00%
Day Count Convention:  Act/365
Term:                  5 years 
  Start date:          2023-01-01 
  Maturity date:       2028-01-01

Here is how you can calculate the Accrued Interest in the date range of [T1,T2) = [2023-01-01, 2024-01-01), which is a regular year:

T1 = 2023-01-01: Starting date (inclusive)
T2 = 2024-01-01: Ending date (exclusive) of the Accrual Range 
T3 = 2023-02-01: Ending date (exclusive) of the Accrual Period  
T4 = 2028-01-01: Ending date (exclusive) of the Accrual Year

DiR(T1,T2) = DiR(T1,T2) 
  = Calendar_Days(T1,T2) 
  = 365

DiY(T1,T2) = 365 

Day_Count_Factor(T1,T2) = DiR(T1,T2) / DiY(T1,T2)
  = 365 / 365 
  = 1.0

Accrued_Interest = Principal × Interest_Rate × Day_Count_Factor
  = $1,000.00 × 5.0% × 1.0
  = $50.00

Now let's see Accrued Interest in another date range of [T1,T2) = [2024-01-01, 2025-01-01), which is a leap year:

T1 = 2024-01-01: Starting date (inclusive)
T2 = 2025-01-01: Ending date (exclusive) of the Accrual Range 
T3 = 2024-02-01: Ending date (exclusive) of the Accrual Period  
T4 = 2028-01-01: Ending date (exclusive) of the Accrual Year

DiR(T1,T2) = DiR(T1,T2) 
  = Calendar_Days(T1,T2) 
  = 366

DiY(T1,T2) = 365 

Day_Count_Factor(T1,T2) = DiR(T1,T2) / DiY(T1,T2)
  = 366 / 365 
  = 1.0027397260274

Accrued_Interest = Principal × Interest_Rate × Day_Count_Factor
  = $1,000.00 × 5.0% × 1.0027397260274
  = $50.13698630137
  = $50.14 

So you earn an extra interest of $0.14 on a leap year.

 

"Act/365" - Daily Compound Interest

"Act/365" - Cross-Period Accrual

Day Count Convention - "Act/365"

⇑⇑ Day Count Conventions

2026-02-04, ∼151🔥, 0💬