diff --git a/fastapi/routing.py b/fastapi/routing.py
index f3c5026dc..8fdee2c8e 100644
--- a/fastapi/routing.py
+++ b/fastapi/routing.py
@@ -1550,8 +1550,8 @@ class APIRouter(routing.Router):
                     prefix + route.path, route.endpoint, name=route.name
                 )
             elif isinstance(route, routing.Mount):
-                self.mount(prefix + route.path, route.app, route.name)
-
+                self.mount(prefix + router.prefix + route.path, route.app, name=route.name)
+                    
         for handler in router.on_startup:
             self.add_event_handler("startup", handler)
         for handler in router.on_shutdown:
diff --git a/tests/test_router_mount.py b/tests/test_router_mount.py
index 57dbdd3e6..9bee074f4 100644
--- a/tests/test_router_mount.py
+++ b/tests/test_router_mount.py
@@ -1,4 +1,4 @@
-from fastapi import APIRouter, FastAPI
+from fastapi import FastAPI, APIRouter
 from fastapi.testclient import TestClient
 
 
@@ -22,4 +22,4 @@ def test_mount_on_router():
     client = TestClient(app)
 
     assert client.get("/api/app").status_code == 200
-    assert client.get("/api/subapi/sub").status_code == 200
+    assert client.get("/api/subapi/sub").status_code == 200
\ No newline at end of file