Question

An invoice for €2,880 plus default interest of €48.40 was paid on October 28th. Interest rate 5.5%. When was the bill due?

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Corbin

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To find out when the bill was due, we first need to figure out the number of days that passed for the default interest to accumulate to €48.40 at an interest rate of 5.5%.
The formula for simple interest is:
\[ I = P \times r \times t \]
Where:
- \( I \) is the interest amount (€48.40 in this case),
- \( P \) is the principal amount (€2,880),
- \( r \) is the annual interest rate (5.5% or 0.055 when expressed as a decimal),
- \( t \) is the time factor in years.
Since interest is typically calculated on a daily basis for such cases, we'll convert the time factor to days and use a standard year of 365 days (or 366 for leap years). The daily interest rate is \( \frac{0.055}{365} \).
Rearranging the formula to solve for \( t \), we get:
\[ t = \frac{I}{P \times r} \]
Let's calculate the number of days \( t \).
The calculation indicates that the interest accrued over approximately 111.53 days. Since the invoice was paid on October 28th, we need to count backward to find the due date.
Let's calculate the exact due date.
The bill was due approximately on July 8, 2024. This is based on counting back 112 days from the payment date of October 28, 2024, which is the rounded number of days calculated from the default interest.

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