Principal from the repayment

Statement

After $6$ months a person repays a total of $1050\ \text{€}$, including principal and simple interest at $8\%$ per year. How much had they borrowed?

Solution

From $M = C\,(1 + r\,t)$ we get $C = \dfrac{M}{1 + r\,t}$, with $t = 0{.}5$. $C = \frac{1050}{1 + 0{.}08\cdot 0{.}5} = \frac{1050}{1{.}04} \approx \boxed{1009{.}62\ \text{€}}.$