Question

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

Calculate interest as a percentage.

Answer 1

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{$\begin{gathered}\sf \bf{\displaystyle t = (7\:500)/(45\:000 \cdot 500) = (1)/(3000)} \end{gathered}$}`

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{$\begin{gathered}\sf \bf{\displaystyle t = (1)/(3000) \cdot 365 \cdot 100 = 12.16\% } \end{gathered}$}`

Thus, the interest rate is 12.16% per year.