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€45,000 is loaned and after a year, 4 months and 15 days €52,500 is received.
Calculate interest as a percentage.

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We calculate the time in days

$$\bf{365 + 120 + 15 = 500 \text{ days}}$$

We calculate the interest

52 500 € - 45 000 € = 7 500 €

We calculate the interest rate:

$$\large\displaystyle\text{\begin{gathered}\sf \bf{\displaystyle t = \frac{7\:500}{45\:000 \cdot 500} = \frac{1}{3000}} \end{gathered}}$$

However, this is the daily rate of interest. To have the annual rate we must multiply by 365. Also, to have the rate as a percentage, we must multiply by 100:

$$\large\displaystyle\text{\begin{gathered}\sf \bf{\displaystyle t = \frac{1}{3000} \cdot 365 \cdot 100 = 12.16\% } \end{gathered}}$$

Thus, the interest rate is 12.16% per year.
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