Present value and discount

Statement

At a $10\%$ simple interest rate, what is the present value of $2400\ \text{€}$ due in $5$ months? What is the discount?

Solution

The present value is $A = \dfrac{M}{1 + r\,t}$, with $t = \dfrac{5}{12}$. $A = \frac{2400}{1 + 0{.}10\cdot \frac{5}{12}} = \frac{2400}{1{.}041\overline{6}} = \boxed{2304\ \text{€}}.$ The discount is $S = M - A = 2400 - 2304 = \boxed{96\ \text{€}}$.