What is the calculation to give a daily interest rate from an annual APR ?

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My brain is in neutral today and I cannot get my head around nor remember the maths to back out a daily interest rate which, when compounded daily over 365 days, will give the annual APR. I cannot even get Goal Seek in Excel to work today so maybe my PC is having an off day as well !

In case I haven't explained it right, If you invested 10k for 1 year at 5% you would have 500 interest. The daily is not simply 500/365 but neither can I remember how to change this formula around (1+5%/365)^365-1 to give the daily figure, which when compounded daily, equals 5% PA.

Any ideas ?

Maybe it is better explained like this.

If I invested £36500 at 10% then you could say that the interest was £10 per day giving £3500 per year. However, with daily compounding interest, it would not be £10 per day because the interest earned on day 1 would be reinvested on day 2 and then that would be reinvested on day 3 etc.

Thrugelmir

In 30 years of finance, I've never seen daily compound interest charged!

Other than by loan sharks.

[Deleted User]

Having tried to set up my own spreadsheet to emulate the online mortgage calculators, it looks to me that for those lenders who charge daily interest, they actually calculate the interest in the following way. For example for a mortgage of £100,000 at 5% pa, the interest for the first month would be (5/100)/12 x 100,000 = £416.67 If it was a 25 year repayment mortgage then the monthly payment would be £584.59 so the amount of capital paid in month 1 would be £167.92. For month 2 your outstanding balance is £99832.08 so the interest calculation for month 2 is (5/100)/12 x 99832.08 = £415.97. Don't know if this helps or not.

Thrugelmir

CR10 wrote: »

Having tried to set up my own spreadsheet to emulate the online mortgage calculators, it looks to me that for those lenders who charge daily interest, they actually calculate the interest in the following way. For example for a mortgage of £100,000 at 5% pa, the interest for the first month would be (5/100)/12 x 100,000 = £416.67 If it was a 25 year repayment mortgage then the monthly payment would be £584.59 so the amount of capital paid in month 1 would be £167.92. For month 2 your outstanding balance is £99832.08 so the interest calculation for month 2 is (5/100)/12 x 99832.08 = £415.97. Don't know if this helps or not.

To calculate it daily , you need to base it on the actual number of days in the month. Your calculalation is monthly.

[Deleted User]

Thrugelmir wrote: »

To calculate it daily , you need to base it on the actual number of days in the month. Your calculalation is monthly.

Thanks for that. That explains why my numbers are marginally different to some of the calculators.