fix(ui): tarifs publics unifiés et prix annuel lisible

La page tarifs reprend la barre du site public. En annuel, Pro affiche
8,25 € par mois (99 € l’année), plus le 99 € comme gros chiffre.

Co-authored-by: Cursor <cursoragent@cursor.com>

memento-note/lib/billing/price-catalog.ts

@@ -0,0 +1,47 @@
+export type BillingTier = 'PRO' | 'BUSINESS'
+export type BillingInterval = 'month' | 'year'
+
+export interface DynamicPrice {
+  display: string
+  amount: number
+  currency: string
+}
+
+export const DEFAULT_PRICES: Record<BillingTier, Record<BillingInterval, DynamicPrice>> = {
+  PRO: {
+    month: { display: '9,90 €', amount: 9.9, currency: 'EUR' },
+    year: { display: '99,00 €', amount: 99, currency: 'EUR' },
+  },
+  BUSINESS: {
+    month: { display: '29,90 €', amount: 29.9, currency: 'EUR' },
+    year: { display: '299,00 €', amount: 299, currency: 'EUR' },
+  },
+}
+
+export function formatBillingAmount(amount: number, currency = 'EUR'): string {
+  const c = currency.toUpperCase()
+  if (c === 'EUR') {
+    return `${amount.toLocaleString('fr-FR', { minimumFractionDigits: 2, maximumFractionDigits: 2 })} €`
+  }
+  if (c === 'USD') {
+    return `$${amount.toLocaleString('en-US', { minimumFractionDigits: 2, maximumFractionDigits: 2 })}`
+  }
+  if (c === 'GBP') {
+    return `£${amount.toLocaleString('en-GB', { minimumFractionDigits: 2, maximumFractionDigits: 2 })}`
+  }
+  return `${amount.toLocaleString('fr-FR', { minimumFractionDigits: 2, maximumFractionDigits: 2 })} ${c}`
+}
+
+/** Prix annuel ramené au mois (99 € / an → 8,25 € / mois). */
+export function yearToMonthlyEquivalent(yearAmount: number): number {
+  return Math.round((yearAmount / 12) * 100) / 100
+}
+
+/** Remise réelle : 9,90 € × 12 vs 99 € / an → 17 %. */
+export function annualDiscountPercent(monthlyAmount: number, yearlyAmount: number): number {
+  const paidMonthlyForYear = monthlyAmount * 12
+  if (paidMonthlyForYear <= 0) return 0
+  const raw = (1 - yearlyAmount / paidMonthlyForYear) * 100
+  if (!Number.isFinite(raw) || raw <= 0) return 0
+  return Math.round(raw)
+}