A tenant pays rent of £1400 on the 21st of each month. They have been paying it late now for 8 months, on the 10th of the following month with an additional £20 on top. I just wanted to confirm the method to work out what loan rate this would be equal to.
Would it be 365/16 days, as the number of days in a year over the days "borrowed" for each month. Then multiplying this by £1400 and £20 to extrapolate?
The number of days varies by the number of days in the month the rent is due. If the rent is for a $31$ day month, the payment is $20$ days late.
Assuming a $30$ day month, they have borrowed $1400$ for $19$ days. At an interest rate of $i\%$ per year, the interest due would be $\frac {19}{365} \cdot \frac i{100} \cdot 1400$. Setting this equal to $20$ gives $i=\frac{20 \cdot 100 \cdot 365}{19 \cdot 1400}\approx 27.44$