Annuity when calculating interest for actual days per month

[Tri Pe]

Hi,

I'm trying to figure out how to calculate an annuity for, say a mortgage, when using actual days (act/360) per month to calculate the interest.

Example:

Loan amount: 500.000
Yearly interest: 10%
Repayment time: 40 years = 480 months

So lets say that the loan is paid out on jan 1st of 2022. The number of interest days in Jan 2022 is 31, for Feb 2022 28, for Mar 2022 31, for Apr 2022 30 etc.

You can calculate a daily interest and then multiply that by the number of days in any given month, but then I can't calculate an annuity so that the monthly amount would result in a payment plan that would be 480 months. If the last month would differ a bit doesn't matter but the number of payment would need to be the given 480.

 

[BadgerRoad]

By annuity I'm assuming you mean the present value of an annuity such as the PV function for unit periods. There isn't one for actual days as it would change for every term and every effective date. The best approach that I am aware of it to build an actual day amortization schedule and iterate on the payment using something like Goal Seek or Solver.

 

[Tri Pe]

By annuity I'm assuming you mean the present value of an annuity such as the PV function for unit periods. There isn't one for actual days as it would change for every term and every effective date. The best approach that I am aware of it to build an actual day amortization schedule and iterate on the payment using something like Goal Seek or Solver.

Yes, goal seek works fine, thanks. The problem with long repayment times and relative high interests is that it results in "negative" amortizations for months with 31 days which doesn't make sense logically but that is a different story.

 

[BadgerRoad]

Actually, it does make sense. That's one of the reasons why mortgage loans use unit period calculations.