Bank commercial discount

Statement

A bank applies a bank discount (interest in advance) of $13\%$ per year. How much does a borrower receive who asks for a loan of $1500\ \text{€}$ to be repaid in $6$ months?

Solution

With bank discount the interest is computed on the final value $M$: the proceeds are $P = M\,(1 - d\,t)$, with $t = 0{.}5$. $P = 1500\,(1 - 0{.}13\cdot 0{.}5) = 1500\cdot 0{.}935 = \boxed{1402{.}50\ \text{€}}.$