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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?

Amy Rose
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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 $i=\frac{20 \cdot 100 \cdot 365}{19 \cdot 1400}\approx 27.44$

Ross Millikan
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  • Is this the same for the 8 months? – Amy Rose Mar 09 '17 at 15:47
  • It varies depending on the length of the month, as I said. The fact that it is repeated $8$ times does not matter. Each is a separate transaction with an interest rate not too different from this. – Ross Millikan Mar 09 '17 at 15:52